Torsions n=2

Torsion Subgroups of B2(G)

This is a list of torsion of B_2(G) for some Zn and Zn+Zn:


Torsion of B_2(Z/2) is:
Abelian Group of order 1


Torsion of B_2(Z/3) is:
Abelian Group of order 1


Torsion of B_2(Z/4) is:
Abelian Group of order 1


Torsion of B_2(Z/5) is:
Abelian Group of order 1


Torsion of B_2(Z/6) is:
Abelian Group isomorphic to Z/2


Torsion of B_2(Z/7) is:
Abelian Group isomorphic to Z/2


Torsion of B_2(Z/8) is:
Abelian Group isomorphic to Z/4


Torsion of B_2(Z/9) is:
Abelian Group isomorphic to Z/3


Torsion of B_2(Z/10) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/6


Torsion of B_2(Z/11) is:
Abelian Group isomorphic to Z/5


Torsion of B_2(Z/12) is:
Abelian Group isomorphic to Z/8


Torsion of B_2(Z/13) is:
Abelian Group isomorphic to Z/7


Torsion of B_2(Z/14) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/12


Torsion of B_2(Z/15) is:
Abelian Group isomorphic to Z/8


Torsion of B_2(Z/16) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/16


Torsion of B_2(Z/17) is:
Abelian Group isomorphic to Z/24


Torsion of B_2(Z/18) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/18


Torsion of B_2(Z/19) is:
Abelian Group isomorphic to Z/15


Torsion of B_2(Z/20) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/24


Torsion of B_2(Z/21) is:
Abelian Group isomorphic to Z/16


Torsion of B_2(Z/22) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/30
Defined on 9 generators 


Torsion of B_2(Z/23) is:
Abelian Group isomorphic to Z/22
Defined on 1 generator


Torsion of B_2(Z/24) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/32
Defined on 3 generators



Torsion of B_2(Z/25) is:
Abelian Group isomorphic to Z/25
Defined on 1 generator


Torsion of B_2(Z/26) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/42
Defined on 11 generators


Torsion of B_2(Z/27) is:
Abelian Group isomorphic to Z/27


Torsion of B_2(Z/28) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/48
Defined on 5 generators  


Torsion of B_2(Z/29) is:
Abelian Group isomorphic to Z/35


Torsion of B_2(Z/30) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/48
Defined on 7 


Torsion of B_2(Z/31) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/40
Defined on 3 generators 


Torsion of B_2(Z/32) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/64
Defined on 7 generators 


Torsion of B_2(Z/33) is:
Abelian Group isomorphic to Z/80
Defined on 1 generator


Torsion of B_2(Z/34) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/72
Defined on 15 generators


Torsion of B_2(Z/35) is:
Abelian Group isomorphic to Z/48
Defined on 1 generator


Torsion of B_2(Z/36) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/72
Defined on 5 generators


Torsion of B_2(Z/37) is:
Abelian Group isomorphic to Z/57
Defined on 1 generator


Torsion of B_2(Z/38) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/90
Defined on 17 generators


Torsion of B_2(Z/39) is:
Abelian Group isomorphic to Z/56
Defined on 1 generator 


Torsion of B_2(Z/40) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/96
Defined on 7 generators


Torsion of B_2(Z/41) is:
Abelian Group isomorphic to Z/140
Defined on 1 generator 


Torsion of B_2(Z/42) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/96
Defined on 11 generators


Torsion of B_2(Z/43) is:
Abelian Group isomorphic to Z/2 + Z/154
Defined on 2 generators


Torsion of B_2(Z/44) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/120
Defined on 9 generators


Torsion of B_2(Z/45) is:
Abelian Group isomorphic to Z/72
Defined on 1 generator 


Torsion of B_2(Z/46) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/132
Defined on 21 generators 


Torsion of B_2(Z/47) is:
Abelian Group isomorphic to Z/92
Defined on 1 generator


Torsion of B_2(Z/48) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/128
Defined on 7 generators 


Torsion of B_2(Z/49) is:
Abelian Group isomorphic to Z/98
Defined on 1 generator 


Torsion of B_2(Z/50) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/150
Defined on 19 generators


Torsion of B_2(Z/51) is:
Abelian Group isomorphic to Z/2 + Z/96
Defined on 2 generators 


Torsion of B_2(Z/52) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/168
Defined on 11 generators


Torsion of B_2(Z/53) is:
Abelian Group isomorphic to Z/117
Defined on 1 generator 


Torsion of B_2(Z/54) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/162
Defined on 17 generators


Torsion of B_2(Z/55) is:
Abelian Group isomorphic to Z/120

 
Torsion of B_2(Z/56) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/192
Defined on 11 generators


Torsion of B_2(Z/57) is:
Abelian Group isomorphic to Z/240
Defined on 1 generator


Torsion of B_2(Z/58) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/210
Defined on 27 generators 


Torsion of B_2(Z/59) is:
Abelian Group isomorphic to Z/145


Torsion of B_2(Z/60) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/192
Defined on 7 generators


Torsion of B_2(Z/61) is:
Abelian Group isomorphic to Z/155


Torsion of B_2(Z/67) is:
Abelian Group isomorphic to Z/187


Torsion of B_2(Z/71) is:
Abelian Group isomorphic to Z/210


Torsion of B_2(Z/73) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/222


Torsion of B_2(Z/79) is:
Abelian Group isomorphic to Z/260


Torsion of B_2(Z/83) is:
Abelian Group isomorphic to Z/287


Torsion of B_2(Z/89) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/330


Torsion of B_2(Z/97) is:
Abelian Group isomorphic to Z/784


Torsion of B_2(Z/113) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/1064


Torsion of B_2(Z/137) is:
Abelian Group isomorphic to Z/1564
Defined on 1 generator in supergroup:








Torsion of B2(Z/2+Z/2) is:
Abelian Group isomorphic to Z/2 + Z/2


Torsion of B2(Z/3+Z/3) is:
Abelian Group of order 1


Torsion of B2(Z/4+Z/4) is:
Abelian Group isomorphic to Z/2


Torsion of B2(Z/5+Z/5) is:
Abelian Group isomorphic to Z/5 + Z/5


Torsion of B2(Z/6+Z/6) is:
Abelian Group isomorphic to Z/6


Torsion of B2(Z/7+Z/7) is:
Abelian Group isomorphic to Z/14 + Z/14 + Z/14



Torsion of B2(Z/8+Z/8) is:
Abelian Group isomorphic to Z/16 + Z/16


Torsion of B2(Z/9+Z/9) is:
Abelian Group isomorphic to Z/27 + Z/27 + Z/27


Torsion of B2(Z/10+Z/10) is:
Abelian Group isomorphic to Z/30 + Z/30


Torsion of B2(Z/11+Z/11) is:
Abelian Group isomorphic to Z/55 + Z/55 + Z/55 + Z/55 + Z/55


Torsion of B2(Z/12+Z/12) is:
Abelian Group isomorphic to Z/48 + Z/48





Torsion Subgroups of B2^-(G)


This is a list of torsion of B_2^-(G) for some Zn and Zn+Zn


Torsion of B2^-(Z/2) is:
Abelian Group of order 1


Torsion of B2^-(Z/3) is:
Abelian Group of order 1


Torsion of B2^-(Z/4) is:
Abelian Group isomorphic to Z/2


Torsion of B2^-(Z/5) is:
Abelian Group isomorphic to Z/2


Torsion of B2^-(Z/6) is:
Abelian Group isomorphic to Z/2 + Z/2


Torsion of B2^-(Z/7) is:
Abelian Group isomorphic to Z/2 + Z/2


Torsion of B2^-(Z/8) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2


Torsion of B2^-(Z/9) is:
Abelian Group isomorphic to Z/2 + Z/2


Torsion of B2^-(Z/10) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 5 generators


Torsion of B2^-(Z/11) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2
Defined on 4 generators


Torsion of B2^-(Z/12) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2
Defined on 3 generators


Torsion of B2^-(Z/13) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 5 generators


Torsion of B2^-(Z/14) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 8 generators


Torsion of B2^-(Z/15) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2
Defined on 3 generators


Torsion of B2^-(Z/16) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 7 generators


Torsion of B2^-(Z/17) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 7 generators 


Torsion of B2^-(Z/18) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 8 generators 


Torsion of B2^-(Z/19) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 8 generators 


Torsion of B2^-(Z/20) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 7 generators


Torsion of B2^-(Z/21) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 5 generators


Torsion of B2^-(Z/22) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 14 generators


Torsion of B2^-(Z/23) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2
Defined on 10 generators 


Torsion of B2^-(Z/24) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 7 generators 


Torsion of B2^-(Z/25) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 9 generators 


Torsion of B2^-(Z/26) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 17 generators 


Torsion of B2^-(Z/27) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 8 generators 


Torsion of B2^-(Z/28) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators


Torsion of B2^-(Z/29) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2
Defined on 13 generators 


Torsion of B2^-(Z/30) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators


Torsion of B2^-(Z/31) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 14 generators


Torsion of B2^-(Z/32) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 15 generators


Torsion of B2^-(Z/33) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 9 generators 


Torsion of B2^-(Z/34) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators 


Torsion of B2^-(Z/35) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators 


Torsion of B2^-(Z/36) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators 



Torsion of B2^-(Z/37) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 17 generators 


Torsion of B2^-(Z/38) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2
Defined on 26 generators


Torsion of B2^-(Z/39) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators


Torsion of B2^-(Z/41) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 19 generators


Torsion of B2^-(Z/42) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 17 generators 



Torsion of B2^-(Z/43) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 20 generators



Torsion of B2^-(Z/44) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 19 generators



Torsion of B2^-(Z/45) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators



Torsion of B2^-(Z/46) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 32 generators 



Torsion of B2^-(Z/47) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 22 generators 



Torsion of B2^-(Z/48) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 15 generators 



Torsion of B2^-(Z/49) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 20 generators 



Torsion of B2^-(Z/50) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 29 generators 


Torsion of B2^-(Z/51) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 15 generators 



Torsion of B2^-(Z/52) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators



Torsion of B2^-(Z/53) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2
Defined on 25 generators 



Torsion of B2^-(Z/54) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2
Defined on 26 generators



Torsion of B2^-(Z/55) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 19 generators 


Torsion of B2^-(Z/56) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators


Torsion of B2^-(Z/57) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 17 generators 



Torsion of B2^-(Z/58) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 41 generators 



Torsion of B2^-(Z/59) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 28 generators



Torsion of B2^-(Z/60) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 15 generators 









Torsion of B2^-(Z/2+Z/2) is:
Abelian Group isomorphic to Z/2 + Z/2


Torsion of B2^-(Z/3+Z/3) is:
Abelian Group of order 1


Torsion of B2^-(Z/4+Z/4) is:
Abelian Group of order 1


Torsion of B2^-(Z/5+Z/5) is:
Abelian Group of order 1


Torsion of B2^-(Z/6+Z/6) is:
Abelian Group of order 1


Torsion of B2^-(Z/7+Z/7) is:
Abelian Group of order 1


Torsion of B2^-(Z/8+Z/8) is:
Abelian Group of order 1


Torsion of B2^-(Z/9+Z/9) is:
Abelian Group of order 1


Torsion of B2^-(Z/10+Z/10) is:
Abelian Group of order 1

Torsion of B2^-(Z/11+Z/11) is:
Abelian Group of order 1


Torsion of B2^-(Z/12+Z/12) is:
Abelian Group of order 1


Torsion of B2^-(Z/13+Z/13) is:
Abelian Group of order 1


Torsion of B2^-(Z/14+Z/14) is:
Abelian Group of order 1


Torsion of B2^-(Z/15+Z/15) is:
Abelian Group of order 1


Torsion of B2^-(Z/16+Z/16) is:
Abelian Group of order 1







Torsion Subgroups of M2(G)


This is a list of torsion of M_2(G) for some Zn and Zn+Zn


Torsion of M_2(Z/1) is:
Abelian Group of order 1


Torsion of M_2(Z/2) is:
Abelian Group isomorphic to Z/2


Torsion of M_2(Z/3) is:
Abelian Group isomorphic to Z/2


Torsion of M_2(Z/4) is:
Abelian Group isomorphic to Z/2 + Z/2


Torsion of M_2(Z/5) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2


Torsion of M_2(Z/6) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2


Torsion of M_2(Z/7) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/4


Torsion of M_2(Z/8) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/4


Torsion of M_2(Z/9) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/6



Torsion of M_2(Z/10) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/6
Defined on 7 generators


Torsion of M_2(Z/11) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/10
Defined on 9 generators


Torsion of M_2(Z/12) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/8
Defined on 5 generators


Torsion of M_2(Z/13) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/14
Defined on 11 generators


Torsion of M_2(Z/14) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/12
Defined on 11 generators


Torsion of M_2(Z/15) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/16
Defined on 7 generators


Torsion of M_2(Z/16) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/16
Defined on 11 generators



Torsion of M_2(Z/17) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/24
Defined on 15 generators 


Torsion of M_2(Z/18) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/18
Defined on 11 generators 


Torsion of M_2(Z/19) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/30
Defined on 17 generators 


Torsion of M_2(Z/20) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/24
Defined on 11 generators


Torsion of M_2(Z/21) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/32
Defined on 11 generators


Torsion of M_2(Z/22) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/30
Defined on 19 generators



Torsion of M_2(Z/23) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/44
Defined on 21 generators 



Torsion of M_2(Z/24) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/32
Defined on 11 generators



Torsion of M_2(Z/25) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/50
Defined on 19 generators



Torsion of M_2(Z/26) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/42
Defined on 23 generators 



Torsion of M_2(Z/27) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/54
Defined on 17 generators



Torsion of M_2(Z/28) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/48
Defined on 17 generators



Torsion of M_2(Z/29) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/70
Defined on 27 generators 



Torsion of M_2(Z/30) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/48
Defined on 15 generators



Torsion of M_2(Z/31) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/80
Defined on 29 generators 



Torsion of M_2(Z/32) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/64
Defined on 23 generators


Torsion of M_2(Z/33) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/80
Defined on 19 generators 



Torsion of M_2(Z/34) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/72
Defined on 31 generators



Torsion of M_2(Z/35) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/96
Defined on 23 generators


Torsion of M_2(Z/36) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/72
Defined on 17 generators


Torsion of M_2(Z/37) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/114
Defined on 35 generators



Torsion of M_2(Z/38) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/90
Defined on 35 generators 



Torsion of M_2(Z/39) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/112
Defined on 23 generators 



Torsion of M_2(Z/40) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/96
Defined on 23 generators



Torsion of M_2(Z/41) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/140
Defined on 39 generators



Torsion of M_2(Z/42) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/96
Defined on 23 generators



Torsion of M_2(Z/43) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/154
Defined on 41 generators



Torsion of M_2(Z/44) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/120
Defined on 29 generators



Torsion of M_2(Z/45) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/144
Defined on 23 generators 



Torsion of M_2(Z/46) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/132
Defined on 43 generators 



Torsion of M_2(Z/47) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/184
Defined on 45 generators



Torsion of M_2(Z/48) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/128
Defined on 23 generators



Torsion of M_2(Z/50) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/150
Defined on 39 generators 



Torsion of M_2(Z/51) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/192
Defined on 31 generators



Torsion of M_2(Z/52) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/168
Defined on 35 generators 



Torsion of M_2(Z/53) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/234
Defined on 51 generators 


Torsion of M_2(Z/54) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/162
Defined on 35 generators


Torsion of M_2(Z/55) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/240
Defined on 39 generators



Torsion of M_2(Z/56) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/192
Defined on 35 generators 



Torsion of M_2(Z/57) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/240
Defined on 35 generators 



Torsion of M_2(Z/58) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/210
Defined on 55 generators 



Torsion of M_2(Z/59) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/290
Defined on 57 generators


Torsion of M_2(Z/60) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/192
Defined on 23 generators 









Torsion of M2(Z/2+Z/2) is:
Abelian Group isomorphic to Z/2 + Z/2


Torsion of M2(Z/3+Z/3) is:
Abelian Group of order 1


Torsion of M2(Z/4+Z/4) is:
Abelian Group isomorphic to Z/2


Torsion of M2(Z/5+Z/5) is:
Abelian Group isomorphic to Z/5 + Z/5



Torsion of M2(Z/6+Z/6) is:
Abelian Group isomorphic to Z/6


Torsion of M2(Z/7+Z/7) is:
Abelian Group isomorphic to Z/14 + Z/14 + Z/14


Torsion of M2(Z/8+Z/8) is:
Abelian Group isomorphic to Z/16 + Z/16


Torsion of M2(Z/9+Z/9) is:
Abelian Group isomorphic to Z/27 + Z/27 + Z/27


Torsion of M2(Z/10+Z/10) is:
Abelian Group isomorphic to Z/30 + Z/30


Torsion of M2(Z/11+Z/11) is:
Abelian Group isomorphic to Z/55 + Z/55 + Z/55 + Z/55 + Z/55


Torsion of M2(Z/12+Z/12) is:
Abelian Group isomorphic to Z/48 + Z/48







Torsion Subgroups of M2^-(G)


This is a list of torsion of M_2^-(G) for some Zn and Zn+Zn

Torsion of M2^-(Z/2) is:
Abelian Group isomorphic to Z/2
Defined on 1 generator



Torsion of M2^-(Z/3) is:
Abelian Group isomorphic to Z/2
Defined on 1 generator



Torsion of M2^-(Z/4) is:
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators


Torsion of M2^-(Z/5) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2
Defined on 3 generators


Torsion of M2^-(Z/6) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2
Defined on 3 generators


Torsion of M2^-(Z/7) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 5 generators



Torsion of M2^-(Z/8) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 5 generators



Torsion of M2^-(Z/9) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 5 generators in supergroup:



Torsion of M2^-(Z/10) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 7 generators



Torsion of M2^-(Z/11) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 9 generators
 


Torsion of M2^-(Z/12) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 5 generators



Torsion of M2^-(Z/13) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators



Torsion of M2^-(Z/14) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators



Torsion of M2^-(Z/15) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 7 generators 


Torsion of M2^-(Z/16) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators




Torsion of M2^-(Z/17) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 15 generators


Torsion of M2^-(Z/18) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators



Torsion of M2^-(Z/19) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 17 generators



Torsion of M2^-(Z/20) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators



Torsion of M2^-(Z/21) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators 



Torsion of M2^-(Z/22) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 19 generators



Torsion of M2^-(Z/23) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 21 generators 



Torsion of M2^-(Z/24) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2
Defined on 11 generators



Torsion of M2^-(Z/25) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 19 generators



Torsion of M2^-(Z/26) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators 



Torsion of M2^-(Z/28) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 17 generators 



Torsion of M2^-(Z/29) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 27 generators



Torsion of M2^-(Z/30) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 15 generators 



Torsion of M2^-(Z/31) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 29 generators



Torsion of M2^-(Z/32) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators



Torsion of M2^-(Z/34) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 31 generators 



Torsion of M2^-(Z/35) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators



Torsion of M2^-(Z/36) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 17 generators




Torsion of M2^-(Z/37) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 35 generators




Torsion of M2^-(Z/38) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 35 generators




Torsion of M2^-(Z/39) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators




Torsion of M2^-(Z/40) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators 



Torsion of M2^-(Z/41) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2
Defined on 39 generators



Torsion of M2^-(Z/42) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators 



Torsion of M2^-(Z/43) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 41 generators 




Torsion of M2^-(Z/44) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 29 generators




Torsion of M2^-(Z/45) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators 




Torsion of M2^-(Z/46) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 43 generators 




Torsion of M2^-(Z/47) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 45 generators 




Torsion of M2^-(Z/48) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators 




Torsion of M2^-(Z/49) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 41 generators



Torsion of M2^-(Z/50) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2
Defined on 39 generators



Torsion of M2^-(Z/51) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 31 generators 



Torsion of M2^-(Z/52) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 35 generators



Torsion of M2^-(Z/53) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2
Defined on 51 generators




Torsion of M2^-(Z/54) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 35 generators 



Torsion of M2^-(Z/55) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2
Defined on 39 generators



Torsion of M2^-(Z/56) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 35 generators




Torsion of M2^-(Z/57) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 35 generators


Torsion of M2^-(Z/58) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 55 generators 




Torsion of M2^-(Z/59) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2
Defined on 57 generators



Torsion of M2^-(Z/60) is:
Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 
+ Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + Z/2 + 
Z/2
Defined on 23 generators






Torsion of M2^-(Z/2+Z/2) is:
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators


Torsion of M2^-(Z/3+Z/3) is:
Abelian Group of order 1



Torsion of M2^-(Z/4+Z/4) is:
Abelian Group of order 1


Torsion of M2^-(Z/5+Z/5) is:
Abelian Group of order 1


Torsion of M2^-(Z/6+Z/6) is:
Abelian Group of order 1


Torsion of M2^-(Z/7+Z/7) is:
Abelian Group of order 1



Torsion of M2^-(Z/8+Z/8) is:
Abelian Group of order 1


Torsion of M2^-(Z/9+Z/9) is:
Abelian Group of order 1


Torsion of M2^-(Z/10+Z/10) is:
Abelian Group of order 1



Torsion of M2^-(Z/11+Z/11) is:
Abelian Group of order 1


Torsion of M2^-(Z/12+Z/12) is:
Abelian Group of order 1


Torsion of M2^-(Z/13+Z/13) is:
Abelian Group of order 1


Torsion of M2^-(Z/14+Z/14) is:
Abelian Group of order 1


Torsion of M2^-(Z/15+Z/15) is:
Abelian Group of order 1



Torsion of M2^-(Z/16+Z/16) is:
Abelian Group of order 1