Ranks n=2
Ranks of B2(G)
These are some tables of ranks of B2(G) for:
1. G=Zn+Zn, n<=40;
2. G=Zn, n<=100;
3. G=Zn+Zm, n,m<=20.
[B2 for Groups of rank 2 Zn+Zn]
[ n, n, Q-rank, Fq-rank... ]
[ 0 0 0 2 3 5 7]
[ 1 1 1 1 1 1 1]
[ 2 2 0 2 0 0 0]
[ 3 3 7 7 7 7 7]
[ 4 4 11 12 11 11 11]
[ 5 5 46 46 46 48 46]
[ 6 6 25 26 26 25 25]
[ 7 7 159 162 159 159 162]
[ 8 8 114 116 114 114 114]
[ 9 9 273 273 276 273 273]
[ 10 10 194 196 196 196 194]
[ 11 11 855 855 855 860 855]
[ 12 12 290 292 292 290 290]
[ 13 13 1602 1602 1602 1602 1608]
[ 14 14 723 726 726 723 726]
[ 15 15 1348 1352 1352 1352 1348]
[ 16 16 1412 1416 1412 1412 1412]
[ 17 17 4424 4432 4432 4424 4424]
[ 18 18 1299 1302 1302 1299 1299]
[ 19 19 6759 6759 6768 6768 6759]
[ 20 20 2500 2504 2504 2504 2500]
[ 21 21 5190 5196 5196 5190 5196]
[ 22 22 4205 4210 4210 4210 4205]
[ 23 23 14047 14058 14047 14047 14047]
[ 24 24 3844 3848 3848 3844 3844]
[ 25 25 15510 15510 15510 15520 15510]
[ 26 26 8070 8076 8076 8070 8076]
[ 27 27 16047 16047 16056 16047 16047]
[ 28 28 9798 9804 9804 9798 9804]
[ 29 29 34314 34314 34314 34328 34328]
[ 30 30 6916 6920 6920 6920 6916]
[ 31 31 44415 44430 44415 44430 44415]
[ 32 32 19464 19472 19464 19464 19464]
[ 33 33 31210 31220 31220 31220 31210]
[ 34 34 23048 23056 23056 23048 23048]
[ 35 35 47244 47256 47256 47256 47256]
[ 36 36 18150 18156 18156 18150 18150]
[ 37 37 88254 88254 88272 88254 88254]
[ 38 38 35649 35658 35658 35658 35649]
[ 39 39 60492 60504 60504 60492 60504]
[ 40 40 35336 35344 35344 35344 35336]
[ 41 41 131620 131620 131620 131620 131620]
[B2 for Cylic Groups Zn]
[ 1, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 1 1 1 1]
[ 1 2 0 0 0 0]
[ 1 3 1 1 1 1]
[ 1 4 1 1 1 1]
[ 1 5 2 2 2 2]
[ 1 6 2 3 2 2]
[ 1 7 3 4 3 3]
[ 1 8 3 4 3 3]
[ 1 9 5 5 6 5]
[ 1 10 4 7 5 4]
[ 1 11 6 6 6 7]
[ 1 12 7 8 7 7]
[ 1 13 8 8 8 8]
[ 1 14 7 12 8 7]
[ 1 15 13 14 13 13]
[ 1 16 10 13 10 10]
[ 1 17 13 14 14 13]
[ 1 18 12 17 13 12]
[ 1 19 16 16 17 17]
[ 1 20 17 20 18 17]
[ 1 21 23 24 23 23]
[ 1 22 16 25 17 17]
[ 1 23 23 24 23 23]
[ 1 24 23 26 23 23]
[ 1 25 30 30 30 31]
[ 1 26 22 33 23 22]
[ 1 27 34 34 35 34]
[ 1 28 31 36 32 31]
[ 1 29 36 36 36 37]
[ 1 30 33 40 34 33]
[ 1 31 41 44 41 42]
[ 1 32 37 44 37 37]
[ 1 33 51 52 51 52]
[ 1 34 37 52 38 37]
[ 1 35 61 62 62 61]
[ 1 36 48 53 49 48]
[ 1 37 58 58 59 58]
[ 1 38 46 63 47 47]
[ 1 39 69 70 69 69]
[ 1 40 61 68 62 61]
[ 1 41 71 72 71 72]
[ 1 42 61 72 62 61]
[ 1 43 78 80 78 78]
[ 1 44 71 80 72 72]
[ 1 45 93 94 94 93]
[ 1 46 67 88 68 67]
[ 1 47 93 94 93 93]
[ 1 48 81 88 81 81]
[ 1 49 108 109 108 108]
[ 1 50 84 103 85 85]
[ 1 51 113 115 114 113]
[ 1 52 97 108 98 97]
[ 1 53 118 118 119 118]
[ 1 54 94 111 95 94]
[ 1 55 141 142 142 142]
[ 1 56 115 126 116 115]
[ 1 57 139 140 140 140]
[ 1 58 106 133 107 107]
[ 1 59 146 146 146 147]
[ 1 60 125 132 126 125]
[ 1 61 156 156 156 157]
[ 1 62 121 150 122 122]
[ 1 63 175 178 176 175]
[ 1 64 141 156 141 141]
[ 1 65 193 196 194 193]
[ 1 66 141 160 142 142]
[ 1 67 188 188 188 188]
[ 1 68 161 176 162 161]
[ 1 69 199 200 199 199]
[ 1 70 169 192 170 169]
[ 1 71 211 212 212 212]
[ 1 72 175 186 176 175]
[ 1 73 223 227 224 223]
[ 1 74 172 207 173 172]
[ 1 75 237 238 237 238]
[ 1 76 199 216 200 200]
[ 1 77 271 272 272 272]
[ 1 78 193 216 194 193]
[ 1 79 261 262 261 262]
[ 1 80 225 240 226 225]
[ 1 81 271 271 272 271]
[ 1 82 211 250 212 212]
[ 1 83 288 288 288 288]
[ 1 84 235 246 236 235]
[ 1 85 321 325 322 321]
[ 1 86 232 273 233 232]
[ 1 87 309 310 309 310]
[ 1 88 271 290 272 272]
[ 1 89 331 335 332 332]
[ 1 90 257 280 258 257]
[ 1 91 373 376 374 373]
[ 1 92 287 308 288 287]
[ 1 93 351 354 351 352]
[ 1 94 277 322 278 277]
[ 1 95 397 398 398 398]
[ 1 96 297 312 297 297]
[ 1 97 393 394 393 393]
[ 1 98 313 354 314 313]
[ 1 99 411 412 412 412]
[ 1 100 341 360 342 342]
[B2(Zm+Zn)]
[ m, n, Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 1 1 1 1]
[ 1 2 0 0 0 0]
[ 1 3 1 1 1 1]
[ 1 4 1 1 1 1]
[ 1 5 2 2 2 2]
[ 1 6 2 3 2 2]
[ 1 7 3 4 3 3]
[ 1 8 3 4 3 3]
[ 1 9 5 5 6 5]
[ 1 10 4 7 5 4]
[ 1 11 6 6 6 7]
[ 1 12 7 8 7 7]
[ 1 13 8 8 8 8]
[ 1 14 7 12 8 7]
[ 1 15 13 14 13 13]
[ 1 16 10 13 10 10]
[ 1 17 13 14 14 13]
[ 1 18 12 17 13 12]
[ 1 19 16 16 17 17]
[ 1 20 17 20 18 17]
[ 2 2 0 2 0 0]
[ 2 4 2 5 2 2]
[ 2 6 3 8 3 3]
[ 2 8 6 13 6 6]
[ 2 10 7 18 8 7]
[ 2 11 16 25 17 17]
[ 2 12 13 20 13 13]
[ 2 13 22 33 23 22]
[ 2 14 13 30 14 13]
[ 2 15 33 40 34 33]
[ 2 16 21 36 21 21]
[ 2 17 37 52 38 37]
[ 2 18 22 39 23 22]
[ 2 19 46 63 47 47]
[ 2 20 33 48 34 33]
[ 3 3 7 7 7 7]
[ 3 6 15 15 16 15]
[ 3 7 23 24 23 23]
[ 3 8 23 26 23 23]
[ 3 9 37 37 38 37]
[ 3 10 33 40 34 33]
[ 3 11 51 52 51 52]
[ 3 12 45 46 46 45]
[ 3 13 69 70 69 69]
[ 3 14 61 72 62 61]
[ 3 15 81 82 82 81]
[ 3 16 81 88 81 81]
[ 3 17 113 115 114 113]
[ 3 18 91 91 92 91]
[ 3 19 139 140 140 140]
[ 3 20 125 132 126 125]
[ 4 4 11 12 11 11]
[ 4 7 31 36 32 31]
[ 4 8 33 34 33 33]
[ 4 9 48 53 49 48]
[ 4 11 71 80 72 72]
[ 4 12 57 58 57 57]
[ 4 13 97 108 98 97]
[ 4 14 61 84 62 61]
[ 4 15 125 132 126 125]
[ 4 16 105 106 105 105]
[ 4 17 161 176 162 161]
[ 4 18 93 116 94 93]
[ 4 19 199 216 200 200]
[ 4 20 145 146 146 145]
[ 5 5 46 46 46 48]
[ 5 6 33 40 34 33]
[ 5 7 61 62 62 61]
[ 5 8 61 68 62 61]
[ 5 9 93 94 94 93]
[ 5 10 110 110 112 112]
[ 5 11 141 142 142 142]
[ 5 12 125 132 126 125]
[ 5 13 193 196 194 193]
[ 5 14 169 192 170 169]
[ 5 15 258 260 258 260]
[ 5 16 225 240 226 225]
[ 5 17 321 325 322 321]
[ 5 18 257 280 258 257]
[ 5 19 397 398 398 398]
[ 5 20 362 364 364 364]
[ 6 6 25 26 26 25]
[ 6 7 61 72 62 61]
[ 6 8 45 60 45 45]
[ 6 10 61 84 62 61]
[ 6 11 141 160 142 142]
[ 6 12 81 82 82 81]
[ 6 13 193 216 194 193]
[ 6 14 115 150 116 115]
[ 6 15 209 210 210 209]
[ 6 16 161 192 161 161]
[ 6 17 321 352 322 321]
[ 6 18 163 164 164 163]
[ 6 19 397 432 398 398]
[ 6 20 241 272 242 241]
[ 7 7 159 162 159 159]
[ 7 8 115 126 116 115]
[ 7 9 175 178 176 175]
[ 7 10 169 192 170 169]
[ 7 11 271 272 272 272]
[ 7 12 235 246 236 235]
[ 7 13 373 376 374 373]
[ 7 14 399 402 402 399]
[ 7 15 457 459 458 457]
[ 7 16 433 456 434 433]
[ 7 17 625 627 626 625]
[ 7 18 493 528 494 493]
[ 7 19 775 778 776 776]
[ 7 20 661 684 662 661]
[ 8 8 114 116 114 114]
[ 8 9 175 186 176 175]
[ 8 10 121 152 122 121]
[ 8 11 271 290 272 272]
[ 8 12 193 194 193 193]
[ 8 13 373 396 374 373]
[ 8 14 229 276 230 229]
[ 8 15 457 472 458 457]
[ 8 16 386 388 386 386]
[ 8 17 625 656 626 625]
[ 8 18 345 392 346 345]
[ 8 19 775 810 776 776]
[ 8 20 513 514 514 513]
[ 9 9 273 273 276 273]
[ 9 10 257 280 258 257]
[ 9 11 411 412 412 412]
[ 9 12 307 308 308 307]
[ 9 13 565 568 566 565]
[ 9 14 493 528 494 493]
[ 9 15 577 578 578 577]
[ 9 16 653 676 654 653]
[ 9 17 945 947 946 945]
[ 9 18 705 705 708 705]
[ 9 19 1171 1176 1172 1172]
[ 9 20 989 1012 990 989]
[ 10 10 194 196 196 196]
[ 10 11 401 440 402 402]
[ 10 12 241 272 242 241]
[ 10 13 553 600 554 553]
[ 10 14 325 396 326 325]
[ 10 15 674 676 676 676]
[ 10 16 449 512 450 449]
[ 10 17 929 992 930 929]
[ 10 18 493 564 494 493]
[ 10 19 1153 1224 1154 1154]
[ 10 20 674 676 676 676]
[ 11 11 855 855 855 860]
[ 11 12 551 570 552 552]
[ 11 13 901 902 902 902]
[ 11 14 781 840 782 782]
[ 11 15 1081 1083 1082 1082]
[ 11 16 1041 1080 1042 1042]
[ 11 17 1521 1523 1522 1522]
[ 11 18 1181 1240 1182 1182]
[ 11 19 1891 1892 1892 1892]
[ 11 20 1581 1620 1582 1582]
[ 12 12 290 292 292 290]
[ 12 13 757 780 758 757]
[ 12 14 457 504 458 457]
[ 12 15 737 738 738 737]
[ 12 16 673 674 673 673]
[ 12 17 1265 1296 1266 1265]
[ 12 18 577 578 578 577]
[ 12 19 1567 1602 1568 1568]
[ 12 20 961 962 962 961]
[ 13 13 1602 1602 1602 1602]
[ 13 14 1081 1152 1082 1081]
[ 13 15 1489 1493 1490 1489]
[ 13 16 1441 1488 1442 1441]
[ 13 17 2113 2117 2114 2113]
[ 13 18 1633 1704 1634 1633]
[ 13 19 2629 2632 2630 2630]
[ 13 20 2185 2232 2186 2185]
[ 14 14 723 726 726 723]
[ 14 15 1297 1344 1298 1297]
[ 14 16 865 960 866 865]
[ 14 17 1825 1920 1826 1825]
[ 14 18 955 1062 956 955]
[ 14 19 2269 2376 2270 2270]
[ 14 20 1297 1392 1298 1297]
[ 15 15 1348 1352 1352 1352]
[ 15 16 1713 1744 1714 1713]
[ 15 17 2497 2505 2498 2497]
[ 15 18 1585 1586 1586 1585]
[ 15 19 3097 3099 3098 3098]
[ 15 20 2402 2404 2404 2404]
[ 16 16 1412 1416 1412 1412]
[ 16 17 2433 2496 2434 2433]
[ 16 18 1297 1392 1298 1297]
[ 16 19 3025 3096 3026 3026]
[ 16 20 1857 1858 1858 1857]
[ 17 17 4424 4432 4432 4424]
[ 17 18 2753 2848 2754 2753]
[ 17 19 4465 4467 4466 4466]
[ 17 20 3681 3744 3682 3681]
[ 18 18 1299 1302 1302 1299]
[ 18 19 3421 3528 3422 3422]
[ 18 20 1937 2032 1938 1937]
[ 19 19 6759 6759 6768 6768]
[ 19 20 4573 4644 4574 4574]
[ 20 20 2500 2504 2504 2504]
Ranks of B2^-(G)
These are some tables of ranks of B_2^-(G) for:
1. G=Zn+Zn, n<=100
2. G=Zn, n<=100
3. G=Zn+Zm, n,m<=10
[B2^- for Groups of rank 2]
[ n, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 1 0 0]
[ 2 2 0 2 0 0]
[ 3 3 3 3 3 3]
[ 4 4 5 5 5 5]
[ 5 5 22 22 22 22]
[ 6 6 13 13 13 13]
[ 7 7 87 87 87 87]
[ 8 8 66 66 66 66]
[ 9 9 165 165 165 165]
[ 10 10 122 122 122 122]
[ 11 11 555 555 555 555]
[ 12 12 194 194 194 194]
[ 13 13 1098 1098 1098 1098]
[ 14 14 507 507 507 507]
[ 15 15 964 964 964 964]
[ 16 16 1028 1028 1028 1028]
[ 17 17 3272 3272 3272 3272]
[ 18 18 975 975 975 975]
[ 19 19 5139 5139 5139 5139]
[ 20 20 1924 1924 1924 1924]
[ 21 21 4038 4038 4038 4038]
[ 22 22 3305 3305 3305 3305]
[ 23 23 11143 11143 11143 11143]
[ 24 24 3076 3076 3076 3076]
[ 25 25 12510 12510 12510 12510]
[ 26 26 6558 6558 6558 6558]
[ 27 27 13131 13131 13131 13131]
[ 28 28 8070 8070 8070 8070]
[ 29 29 28434 28434 28434 28434]
[ 30 30 5764 5764 5764 5764]
[ 31 31 37215 37215 37215 37215]
[ 32 32 16392 16392 16392 16392]
[ 33 33 26410 26410 26410 26410]
[ 34 34 19592 19592 19592 19592]
[ 35 35 40332 40332 40332 40332]
[ 36 36 15558 15558 15558 15558]
[ 37 37 75942 75942 75942 75942]
[ 38 38 30789 30789 30789 30789]
[ 39 39 52428 52428 52428 52428]
[ 40 40 30728 30728 30728 30728]
[ 41 41 114820 114820 114820 114820]
[ 42 42 24198 24198 24198 24198]
[ 43 43 139083 139083 139083 139083]
[ 44 44 52810 52810 52810 52810]
[ 45 45 77772 77772 77772 77772]
[ 46 46 66803 66803 66803 66803]
[ 47 47 198927 198927 198927 198927]
[ 48 48 49160 49160 49160 49160]
[ 49 49 201705 201705 201705 201705]
[ 50 50 75010 75010 75010 75010]
[ 51 51 156688 156688 156688 156688]
52
[104844 104844 104844 104844]
53
[322478 322478 322478 322478]
54
[78741 78741 78741 78741]
55
[264020 264020 264020 264020]
56
[129036 129036 129036 129036]
57
[246258 246258 246258 246258]
58
[170534 170534 170534 170534]
59
[496219 496219 496219 496219]
60
[92168 92168 92168 92168]
61
[567330 567330 567330 567330]
62
[223215 223215 223215 223215]
63
[326610 326610 326610 326610]
64
[262160 262160 262160 262160]
65
[524184 524184 524184 524184]
66
[158410 158410 158410 158410]
67
[826947 826947 826947 826947]
68
[313360 313360 313360 313360]
69
[534358 534358 534358 534358]
70
[241932 241932 241932 241932]
71
[1043735 1043735 1043735 1043735]
72
[248844 248844 248844 248844]
73
[1166868 1166868 1166868 1166868]
74
[455562 455562 455562 455562]
75
[600020 600020 600020 600020]
76
[492498 492498 492498 492498]
77
[1108830 1108830 1108830 1108830]
78
[314508 314508 314508 314508]
79
[1602159 1602159 1602159 1602159]
80
[491536 491536 491536 491536]
81
[1062909 1062909 1062909 1062909]
82
[688820 688820 688820 688820]
83
[1953363 1953363 1953363 1953363]
84
[387084 387084 387084 387084]
85
[1566752 1566752 1566752 1566752]
86
[834393 834393 834393 834393]
87
[1364188 1364188 1364188 1364188]
88
[844820 844820 844820 844820]
89
[2584604 2584604 2584604 2584604]
90
[466572 466572 466572 466572]
91
[2201508 2201508 2201508 2201508]
92
[1068694 1068694 1068694 1068694]
93
[1785630 1785630 1785630 1785630]
94
[1193447 1193447 1193447 1193447]
95
[2462436 2462436 2462436 2462436]
96
[786448 786448 786448 786448]
98
[1210125 1210125 1210125 1210125]
99
[2138430 2138430 2138430 2138430]
100
[1200020 1200020 1200020 1200020]
[B2^- for Cylic Groups]
[ 1, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 1 0 0]
[ 1 2 0 0 0 0]
[ 1 3 0 0 0 0]
[ 1 4 0 1 0 0]
[ 1 5 0 1 0 0]
[ 1 6 0 2 0 0]
[ 1 7 0 2 0 0]
[ 1 8 0 3 0 0]
[ 1 9 1 3 1 1]
[ 1 10 0 5 0 0]
[ 1 11 1 5 1 1]
[ 1 12 2 5 2 2]
[ 1 13 2 7 2 2]
[ 1 14 1 9 1 1]
[ 1 15 5 8 5 5]
[ 1 16 3 10 3 3]
[ 1 17 5 12 5 5]
[ 1 18 4 12 4 4]
[ 1 19 7 15 7 7]
[ 1 20 7 14 7 7]
[ 1 21 11 16 11 11]
[ 1 22 6 20 6 6]
[ 1 23 12 22 12 12]
[ 1 24 11 18 11 11]
[ 1 25 16 25 16 16]
[ 1 26 10 27 10 10]
[ 1 27 19 27 19 19]
[ 1 28 16 27 16 16]
[ 1 29 22 35 22 22]
[ 1 30 17 28 17 17]
[ 1 31 26 40 26 26]
[ 1 32 21 36 21 21]
[ 1 33 31 40 31 31]
[ 1 34 21 44 21 21]
[ 1 35 37 48 37 37]
[ 1 36 28 39 28 28]
[ 1 37 40 57 40 40]
[ 1 38 28 54 28 28]
[ 1 39 45 56 45 45]
[ 1 40 37 52 37 37]
[ 1 41 51 70 51 51]
[ 1 42 37 54 37 37]
[ 1 43 57 77 57 57]
[ 1 44 46 65 46 46]
[ 1 45 61 72 61 61]
[ 1 46 45 77 45 45]
[ 1 47 70 92 70 70]
[ 1 48 53 68 53 53]
[ 1 49 78 98 78 78]
[ 1 50 56 85 56 56]
[ 1 51 81 96 81 81]
[ 1 52 67 90 67 67]
[ 1 53 92 117 92 92]
[ 1 54 64 90 64 64]
[ 1 55 101 120 101 101]
[ 1 56 79 102 79 79]
[ 1 57 103 120 103 103]
[ 1 58 78 119 78 78]
[ 1 59 117 145 117 117]
[ 1 60 85 100 85 85]
[ 1 61 126 155 126 126]
[ 1 62 91 135 91 91]
[ 1 63 127 144 127 127]
[ 1 64 105 136 105 105]
[ 1 65 145 168 145 145]
[ 1 66 101 130 101 101]
[ 1 67 155 187 155 155]
[ 1 68 121 152 121 121]
[ 1 69 155 176 155 155]
[ 1 70 121 156 121 121]
[ 1 71 176 210 176 176]
[ 1 72 127 150 127 127]
[ 1 73 187 222 187 187]
[ 1 74 136 189 136 136]
[ 1 75 181 200 181 181]
[ 1 76 154 189 154 154]
[ 1 77 211 240 211 211]
[ 1 78 145 180 145 145]
[ 1 79 222 260 222 222]
[ 1 80 169 200 169 169]
[ 1 81 217 243 217 217]
[ 1 82 171 230 171 171]
[ 1 83 247 287 247 247]
[ 1 84 175 198 175 175]
[ 1 85 257 288 257 257]
[ 1 86 190 252 190 190]
[ 1 87 253 280 253 253]
[ 1 88 211 250 211 211]
[ 1 89 287 330 287 287]
[ 1 90 193 228 193 193]
[ 1 91 301 336 301 301]
[ 1 92 232 275 232 232]
[ 1 93 291 320 291 291]
[ 1 94 231 299 231 231]
[ 1 95 325 360 325 325]
[ 1 96 233 264 233 233]
[ 1 97 345 392 345 345]
[ 1 98 253 315 253 253]
[ 1 99 331 360 331 331]
[ 1 100 271 310 271 271]
[B^2-]
[ m, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 1 0 0]
[ 1 2 0 0 0 0]
[ 1 3 0 0 0 0]
[ 1 4 0 1 0 0]
[ 1 5 0 1 0 0]
[ 1 6 0 2 0 0]
[ 1 7 0 2 0 0]
[ 1 8 0 3 0 0]
[ 1 9 1 3 1 1]
[ 1 10 0 5 0 0]
[ 2 2 0 2 0 0]
[ 2 4 0 3 0 0]
[ 2 6 0 5 0 0]
[ 2 7 1 9 1 1]
[ 2 8 1 8 1 1]
[ 2 9 4 12 4 4]
[ 2 10 1 12 1 1]
[ 3 3 3 3 3 3]
[ 3 4 2 5 2 2]
[ 3 5 5 8 5 5]
[ 3 6 7 7 7 7]
[ 3 7 11 16 11 11]
[ 3 8 11 18 11 11]
[ 3 9 19 19 19 19]
[ 3 10 17 28 17 17]
[ 4 4 5 5 5 5]
[ 4 5 7 14 7 7]
[ 4 6 5 12 5 5]
[ 4 7 16 27 16 16]
[ 4 8 17 17 17 17]
[ 4 9 28 39 28 28]
[ 4 10 17 32 17 17]
[ 5 5 22 22 22 22]
[ 5 6 17 28 17 17]
[ 5 7 37 48 37 37]
[ 5 8 37 52 37 37]
[ 5 9 61 72 61 61]
[ 5 10 62 62 62 62]
[ 6 6 13 13 13 13]
[ 6 7 37 54 37 37]
[ 6 8 25 40 25 25]
[ 6 9 55 55 55 55]
[ 6 10 37 60 37 37]
[ 7 7 87 87 87 87]
[ 7 8 79 102 79 79]
[ 7 9 127 144 127 127]
[ 7 10 121 156 121 121]
[ 8 8 66 66 66 66]
[ 8 9 127 150 127 127]
[ 8 10 81 112 81 81]
[ 9 9 165 165 165 165]
[ 9 10 193 228 193 193]
[ 10 10 122 122 122 122]
Ranks of M2(G)
These are some tables of ranks of M2(G) for:
1. G=Zn+Zn, n<=40
2. G=Zn, n<=100
3. G=Zn+Zm, n,m<=20
[M2 for Groups of rank 2]
[ n, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 0 0 0]
[ 2 2 0 2 0 0]
[ 3 3 7 7 7 7]
[ 4 4 11 12 11 11]
[ 5 5 46 46 46 48]
[ 6 6 25 26 26 25]
[ 7 7 159 162 159 159]
[ 8 8 114 116 114 114]
[ 9 9 273 273 276 273]
[ 10 10 194 196 196 196]
[ 11 11 855 855 855 860]
[ 12 12 290 292 292 290]
[ 13 13 1602 1602 1602 1602]
[ 14 14 723 726 726 723]
[ 15 15 1348 1352 1352 1352]
[ 16 16 1412 1416 1412 1412]
[ 17 17 4424 4432 4432 4424]
[ 18 18 1299 1302 1302 1299]
[ 19 19 6759 6759 6768 6768]
[ 20 20 2500 2504 2504 2504]
[ 21 21 5190 5196 5196 5190]
[ 22 22 4205 4210 4210 4210]
[ 23 23 14047 14058 14047 14047]
[ 24 24 3844 3848 3848 3844]
[ 25 25 15510 15510 15510 15520]
[ 26 26 8070 8076 8076 8070]
[ 27 27 16047 16047 16056 16047]
[ 28 28 9798 9804 9804 9798]
[ 29 29 34314 34314 34314 34328]
[ 30 30 6916 6920 6920 6920]
[ 31 31 44415 44430 44415 44430]
[ 32 32 19464 19472 19464 19464]
[ 33 33 31210 31220 31220 31220]
[ 34 34 23048 23056 23056 23048]
[ 35 35 47244 47256 47256 47256]
[ 36 36 18150 18156 18156 18150]
[ 37 37 88254 88254 88272 88254]
[ 38 38 35649 35658 35658 35658]
[ 39 39 60492 60504 60504 60492]
[ 40 40 35336 35344 35344 35344]
[M2 for Cylic Groups]
[ 1, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 0 0 0]
[ 1 2 0 1 0 0]
[ 1 3 1 2 1 1]
[ 1 4 1 3 1 1]
[ 1 5 2 5 2 2]
[ 1 6 2 5 2 2]
[ 1 7 3 8 3 3]
[ 1 8 3 8 3 3]
[ 1 9 5 10 6 5]
[ 1 10 4 11 5 4]
[ 1 11 6 15 6 7]
[ 1 12 7 12 7 7]
[ 1 13 8 19 8 8]
[ 1 14 7 18 8 7]
[ 1 15 13 20 13 13]
[ 1 16 10 21 10 10]
[ 1 17 13 28 14 13]
[ 1 18 12 23 13 12]
[ 1 19 16 33 17 17]
[ 1 20 17 28 18 17]
[ 1 21 23 34 23 23]
[ 1 22 16 35 17 17]
[ 1 23 23 44 23 23]
[ 1 24 23 34 23 23]
[ 1 25 30 49 30 31]
[ 1 26 22 45 23 22]
[ 1 27 34 51 35 34]
[ 1 28 31 48 32 31]
[ 1 29 36 63 36 37]
[ 1 30 33 48 34 33]
[ 1 31 41 70 41 42]
[ 1 32 37 60 37 37]
[ 1 33 51 70 51 52]
[ 1 34 37 68 38 37]
[ 1 35 61 84 62 61]
[ 1 36 48 65 49 48]
[ 1 37 58 93 59 58]
[ 1 38 46 81 47 47]
[ 1 39 69 92 69 69]
[ 1 40 61 84 62 61]
[ 1 41 71 110 71 72]
[ 1 42 61 84 62 61]
[ 1 43 78 119 78 78]
[ 1 44 71 100 72 72]
[ 1 45 93 116 94 93]
[ 1 46 67 110 68 67]
[ 1 47 93 138 93 93]
[ 1 48 81 104 81 81]
[ 1 49 108 149 108 108]
[ 1 50 84 123 85 85]
[ 1 51 113 144 114 113]
[ 1 52 97 132 98 97]
[ 1 53 118 169 119 118]
[ 1 54 94 129 95 94]
[ 1 55 141 180 142 142]
[ 1 56 115 150 116 115]
[ 1 57 139 174 140 140]
[ 1 58 106 161 107 107]
[ 1 59 146 203 146 147]
[ 1 60 125 148 126 125]
[ 1 61 156 215 156 157]
[ 1 62 121 180 122 122]
[ 1 63 175 210 176 175]
[ 1 64 141 188 141 141]
[ 1 65 193 240 194 193]
[ 1 66 141 180 142 142]
[ 1 67 188 253 188 188]
[ 1 68 161 208 162 161]
[ 1 69 199 242 199 199]
[ 1 70 169 216 170 169]
[ 1 71 211 280 212 212]
[ 1 72 175 210 176 175]
[ 1 73 223 294 224 223]
[ 1 74 172 243 173 172]
[ 1 75 237 276 237 238]
[ 1 76 199 252 200 200]
[ 1 77 271 330 272 272]
[ 1 78 193 240 194 193]
[ 1 79 261 338 261 262]
[ 1 80 225 272 226 225]
[ 1 81 271 324 272 271]
[ 1 82 211 290 212 212]
[ 1 83 288 369 288 288]
[ 1 84 235 270 236 235]
[ 1 85 321 384 322 321]
[ 1 86 232 315 233 232]
[ 1 87 309 364 309 310]
[ 1 88 271 330 272 272]
[ 1 89 331 418 332 332]
[ 1 90 257 304 258 257]
[ 1 91 373 444 374 373]
[ 1 92 287 352 288 287]
[ 1 93 351 410 351 352]
[ 1 94 277 368 278 277]
[ 1 95 397 468 398 398]
[ 1 96 297 344 297 297]
[ 1 97 393 488 393 393]
[ 1 98 313 396 314 313]
[ 1 99 411 470 412 412]
[ 1 100 341 400 342 342]
[M2 for Zm+Zn]
[ m, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 0 0 0]
[ 1 2 0 1 0 0]
[ 1 3 1 2 1 1]
[ 1 4 1 3 1 1]
[ 1 5 2 5 2 2]
[ 1 6 2 5 2 2]
[ 1 7 3 8 3 3]
[ 1 8 3 8 3 3]
[ 1 9 5 10 6 5]
[ 1 10 4 11 5 4]
[ 1 11 6 15 6 7]
[ 1 12 7 12 7 7]
[ 1 13 8 19 8 8]
[ 1 14 7 18 8 7]
[ 1 15 13 20 13 13]
[ 1 16 10 21 10 10]
[ 1 17 13 28 14 13]
[ 1 18 12 23 13 12]
[ 1 19 16 33 17 17]
[ 1 20 17 28 18 17]
[ 2 2 0 2 0 0]
[ 2 4 2 5 2 2]
[ 2 6 3 8 3 3]
[ 2 8 6 13 6 6]
[ 2 10 7 18 8 7]
[ 2 11 16 35 17 17]
[ 2 12 13 20 13 13]
[ 2 13 22 45 23 22]
[ 2 14 13 30 14 13]
[ 2 15 33 48 34 33]
[ 2 16 21 36 21 21]
[ 2 17 37 68 38 37]
[ 2 18 22 39 23 22]
[ 2 19 46 81 47 47]
[ 2 20 33 48 34 33]
[ 3 3 7 7 7 7]
[ 3 6 15 15 16 15]
[ 3 7 23 34 23 23]
[ 3 8 23 34 23 23]
[ 3 9 37 37 38 37]
[ 3 10 33 48 34 33]
[ 3 11 51 70 51 52]
[ 3 12 45 46 46 45]
[ 3 13 69 92 69 69]
[ 3 14 61 84 62 61]
[ 3 15 81 82 82 81]
[ 3 16 81 104 81 81]
[ 3 17 113 144 114 113]
[ 3 18 91 91 92 91]
[ 3 19 139 174 140 140]
[ 3 20 125 148 126 125]
[ 4 4 11 12 11 11]
[ 4 7 31 48 32 31]
[ 4 8 33 34 33 33]
[ 4 9 48 65 49 48]
[ 4 11 71 100 72 72]
[ 4 12 57 58 57 57]
[ 4 13 97 132 98 97]
[ 4 14 61 84 62 61]
[ 4 15 125 148 126 125]
[ 4 16 105 106 105 105]
[ 4 17 161 208 162 161]
[ 4 18 93 116 94 93]
[ 4 19 199 252 200 200]
[ 4 20 145 146 146 145]
[ 5 5 46 46 46 48]
[ 5 6 33 48 34 33]
[ 5 7 61 84 62 61]
[ 5 8 61 84 62 61]
[ 5 9 93 116 94 93]
[ 5 10 110 110 112 112]
[ 5 11 141 180 142 142]
[ 5 12 125 148 126 125]
[ 5 13 193 240 194 193]
[ 5 14 169 216 170 169]
[ 5 15 258 260 258 260]
[ 5 16 225 272 226 225]
[ 5 17 321 384 322 321]
[ 5 18 257 304 258 257]
[ 5 19 397 468 398 398]
[ 5 20 362 364 364 364]
[ 6 6 25 26 26 25]
[ 6 7 61 84 62 61]
[ 6 8 45 60 45 45]
[ 6 10 61 84 62 61]
[ 6 11 141 180 142 142]
[ 6 12 81 82 82 81]
[ 6 13 193 240 194 193]
[ 6 14 115 150 116 115]
[ 6 15 209 210 210 209]
[ 6 16 161 192 161 161]
[ 6 17 321 384 322 321]
[ 6 18 163 164 164 163]
[ 6 19 397 468 398 398]
[ 6 20 241 272 242 241]
[ 7 7 159 162 159 159]
[ 7 8 115 150 116 115]
[ 7 9 175 210 176 175]
[ 7 10 169 216 170 169]
[ 7 11 271 330 272 272]
[ 7 12 235 270 236 235]
[ 7 13 373 444 374 373]
[ 7 14 399 402 402 399]
[ 7 15 457 504 458 457]
[ 7 16 433 504 434 433]
[ 7 17 625 720 626 625]
[ 7 18 493 564 494 493]
[ 7 19 775 882 776 776]
[ 7 20 661 732 662 661]
[ 8 8 114 116 114 114]
[ 8 9 175 210 176 175]
[ 8 10 121 152 122 121]
[ 8 11 271 330 272 272]
[ 8 12 193 194 193 193]
[ 8 13 373 444 374 373]
[ 8 14 229 276 230 229]
[ 8 15 457 504 458 457]
[ 8 16 386 388 386 386]
[ 8 17 625 720 626 625]
[ 8 18 345 392 346 345]
[ 8 19 775 882 776 776]
[ 8 20 513 514 514 513]
[ 9 9 273 273 276 273]
[ 9 10 257 304 258 257]
[ 9 11 411 470 412 412]
[ 9 12 307 308 308 307]
[ 9 13 565 636 566 565]
[ 9 14 493 564 494 493]
[ 9 15 577 578 578 577]
[ 9 16 653 724 654 653]
[ 9 17 945 1040 946 945]
[ 9 18 705 705 708 705]
[ 9 19 1171 1278 1172 1172]
[ 9 20 989 1060 990 989]
[ 10 10 194 196 196 196]
[ 10 11 401 480 402 402]
[ 10 12 241 272 242 241]
[ 10 13 553 648 554 553]
[ 10 14 325 396 326 325]
[ 10 15 674 676 676 676]
[ 10 16 449 512 450 449]
[ 10 17 929 1056 930 929]
[ 10 18 493 564 494 493]
[ 10 19 1153 1296 1154 1154]
[ 10 20 674 676 676 676]
[ 11 11 855 855 855 860]
[ 11 12 551 610 552 552]
[ 11 13 901 1020 902 902]
[ 11 14 781 900 782 782]
[ 11 15 1081 1160 1082 1082]
[ 11 16 1041 1160 1042 1042]
[ 11 17 1521 1680 1522 1522]
[ 11 18 1181 1300 1182 1182]
[ 11 19 1891 2070 1892 1892]
[ 11 20 1581 1700 1582 1582]
[ 12 12 290 292 292 290]
[ 12 13 757 828 758 757]
[ 12 14 457 504 458 457]
[ 12 15 737 738 738 737]
[ 12 16 673 674 673 673]
[ 12 17 1265 1360 1266 1265]
[ 12 18 577 578 578 577]
[ 12 19 1567 1674 1568 1568]
[ 12 20 961 962 962 961]
[ 13 13 1602 1602 1602 1602]
[ 13 14 1081 1224 1082 1081]
[ 13 15 1489 1584 1490 1489]
[ 13 16 1441 1584 1442 1441]
[ 13 17 2113 2304 2114 2113]
[ 13 18 1633 1776 1634 1633]
[ 13 19 2629 2844 2630 2630]
[ 13 20 2185 2328 2186 2185]
[ 14 14 723 726 726 723]
[ 14 15 1297 1392 1298 1297]
[ 14 16 865 960 866 865]
[ 14 17 1825 2016 1826 1825]
[ 14 18 955 1062 956 955]
[ 14 19 2269 2484 2270 2270]
[ 14 20 1297 1392 1298 1297]
[ 15 15 1348 1352 1352 1352]
[ 15 16 1713 1808 1714 1713]
[ 15 17 2497 2624 2498 2497]
[ 15 18 1585 1586 1586 1585]
[ 15 19 3097 3240 3098 3098]
[ 15 20 2402 2404 2404 2404]
[ 16 16 1412 1416 1412 1412]
[ 16 17 2433 2624 2434 2433]
[ 16 18 1297 1392 1298 1297]
[ 16 19 3025 3240 3026 3026]
[ 16 20 1857 1858 1858 1857]
[ 17 17 4424 4432 4432 4424]
[ 17 18 2753 2944 2754 2753]
[ 17 19 4465 4752 4466 4466]
[ 17 20 3681 3872 3682 3681]
[ 18 18 1299 1302 1302 1299]
[ 18 19 3421 3636 3422 3422]
[ 18 20 1937 2032 1938 1937]
[ 19 19 6759 6759 6768 6768]
[ 19 20 4573 4788 4574 4574]
[ 20 20 2500 2504 2504 2504]
Ranks of M2^-(G)
These are some tables of ranks of M_2^-(G) for:
1. G=Zn+Zn, n<=40
2. G=Zn, n<=100
3. G=Zn+Zm, n,m<=10
[M2^- for Groups of rank 2]
[ n, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 0 0 0]
[ 2 2 0 2 0 0]
[ 3 3 3 3 3 3]
[ 4 4 5 5 5 5]
[ 5 5 22 22 22 22]
[ 6 6 13 13 13 13]
[ 7 7 87 87 87 87]
[ 8 8 66 66 66 66]
[ 9 9 165 165 165 165]
[ 10 10 122 122 122 122]
[ 11 11 555 555 555 555]
[ 12 12 194 194 194 194]
[ 13 13 1098 1098 1098 1098]
[ 14 14 507 507 507 507]
[ 15 15 964 964 964 964]
[ 16 16 1028 1028 1028 1028]
[ 17 17 3272 3272 3272 3272]
[ 18 18 975 975 975 975]
[ 19 19 5139 5139 5139 5139]
[ 20 20 1924 1924 1924 1924]
[ 21 21 4038 4038 4038 4038]
[ 22 22 3305 3305 3305 3305]
[ 23 23 11143 11143 11143 11143]
[ 24 24 3076 3076 3076 3076]
[ 25 25 12510 12510 12510 12510]
[ 26 26 6558 6558 6558 6558]
[ 27 27 13131 13131 13131 13131]
[ 28 28 8070 8070 8070 8070]
[ 29 29 28434 28434 28434 28434]
[ 30 30 5764 5764 5764 5764]
[ 31 31 37215 37215 37215 37215]
[ 32 32 16392 16392 16392 16392]
[ 33 33 26410 26410 26410 26410]
[ 34 34 19592 19592 19592 19592]
[ 35 35 40332 40332 40332 40332]
[ 36 36 15558 15558 15558 15558]
[ 37 37 75942 75942 75942 75942]
[ 38 38 30789 30789 30789 30789]
[ 39 39 52428 52428 52428 52428]
[ 40 40 30728 30728 30728 30728]
[[M2^- for Cyclic Groups]
[ 1, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 0 0 0]
[ 1 2 0 1 0 0]
[ 1 3 0 1 0 0]
[ 1 4 0 2 0 0]
[ 1 5 0 3 0 0]
[ 1 6 0 3 0 0]
[ 1 7 0 5 0 0]
[ 1 8 0 5 0 0]
[ 1 9 1 6 1 1]
[ 1 10 0 7 0 0]
[ 1 11 1 10 1 1]
[ 1 12 2 7 2 2]
[ 1 13 2 13 2 2]
[ 1 14 1 12 1 1]
[ 1 15 5 12 5 5]
[ 1 16 3 14 3 3]
[ 1 17 5 20 5 5]
[ 1 18 4 15 4 4]
[ 1 19 7 24 7 7]
[ 1 20 7 18 7 7]
[ 1 21 11 22 11 11]
[ 1 22 6 25 6 6]
[ 1 23 12 33 12 12]
[ 1 24 11 22 11 11]
[ 1 25 16 35 16 16]
[ 1 26 10 33 10 10]
[ 1 27 19 36 19 19]
[ 1 28 16 33 16 16]
[ 1 29 22 49 22 22]
[ 1 30 17 32 17 17]
[ 1 31 26 55 26 26]
[ 1 32 21 44 21 21]
[ 1 33 31 50 31 31]
[ 1 34 21 52 21 21]
[ 1 35 37 60 37 37]
[ 1 36 28 45 28 28]
[ 1 37 40 75 40 40]
[ 1 38 28 63 28 28]
[ 1 39 45 68 45 45]
[ 1 40 37 60 37 37]
[ 1 41 51 90 51 51]
[ 1 42 37 60 37 37]
[ 1 43 57 98 57 57]
[ 1 44 46 75 46 46]
[ 1 45 61 84 61 61]
[ 1 46 45 88 45 45]
[ 1 47 70 115 70 70]
[ 1 48 53 76 53 53]
[ 1 49 78 119 78 78]
[ 1 50 56 95 56 56]
[ 1 51 81 112 81 81]
[ 1 52 67 102 67 67]
[ 1 53 92 143 92 92]
[ 1 54 64 99 64 64]
[ 1 55 101 140 101 101]
[ 1 56 79 114 79 79]
[ 1 57 103 138 103 103]
[ 1 58 78 133 78 78]
[ 1 59 117 174 117 117]
[ 1 60 85 108 85 85]
[ 1 61 126 185 126 126]
[ 1 62 91 150 91 91]
[ 1 63 127 162 127 127]
[ 1 64 105 152 105 105]
[ 1 65 145 192 145 145]
[ 1 66 101 140 101 101]
[ 1 67 155 220 155 155]
[ 1 68 121 168 121 121]
[ 1 69 155 198 155 155]
[ 1 70 121 168 121 121]
[ 1 71 176 245 176 176]
[ 1 72 127 162 127 127]
[ 1 73 187 258 187 187]
[ 1 74 136 207 136 136]
[ 1 75 181 220 181 181]
[ 1 76 154 207 154 154]
[ 1 77 211 270 211 211]
[ 1 78 145 192 145 145]
[ 1 79 222 299 222 222]
[ 1 80 169 216 169 169]
[ 1 81 217 270 217 217]
[ 1 82 171 250 171 171]
[ 1 83 247 328 247 247]
[ 1 84 175 210 175 175]
[ 1 85 257 320 257 257]
[ 1 86 190 273 190 190]
[ 1 87 253 308 253 253]
[ 1 88 211 270 211 211]
[ 1 89 287 374 287 287]
[ 1 90 193 240 193 193]
[ 1 91 301 372 301 301]
[ 1 92 232 297 232 232]
[ 1 93 291 350 291 291]
[ 1 94 231 322 231 231]
[ 1 95 325 396 325 325]
[ 1 96 233 280 233 233]
[ 1 97 345 440 345 345]
[ 1 98 253 336 253 253]
[ 1 99 331 390 331 331]
[ 1 100 271 330 271 271]
[M2^-]
[ m, n,Q-rank,Fq-rank...]
[ 0 0 0 2 3 5]
[ 1 1 0 0 0 0]
[ 1 2 0 1 0 0]
[ 1 3 0 1 0 0]
[ 1 4 0 2 0 0]
[ 1 5 0 3 0 0]
[ 1 6 0 3 0 0]
[ 1 7 0 5 0 0]
[ 1 8 0 5 0 0]
[ 1 9 1 6 1 1]
[ 1 10 0 7 0 0]
[ 2 2 0 2 0 0]
[ 2 4 0 3 0 0]
[ 2 6 0 5 0 0]
[ 2 7 1 12 1 1]
[ 2 8 1 8 1 1]
[ 2 9 4 15 4 4]
[ 2 10 1 12 1 1]
[ 3 3 3 3 3 3]
[ 3 4 2 7 2 2]
[ 3 5 5 12 5 5]
[ 3 6 7 7 7 7]
[ 3 7 11 22 11 11]
[ 3 8 11 22 11 11]
[ 3 9 19 19 19 19]
[ 3 10 17 32 17 17]
[ 4 4 5 5 5 5]
[ 4 5 7 18 7 7]
[ 4 6 5 12 5 5]
[ 4 7 16 33 16 16]
[ 4 8 17 17 17 17]
[ 4 9 28 45 28 28]
[ 4 10 17 32 17 17]
[ 5 5 22 22 22 22]
[ 5 6 17 32 17 17]
[ 5 7 37 60 37 37]
[ 5 8 37 60 37 37]
[ 5 9 61 84 61 61]
[ 5 10 62 62 62 62]
[ 6 6 13 13 13 13]
[ 6 7 37 60 37 37]
[ 6 8 25 40 25 25]
[ 6 9 55 55 55 55]
[ 6 10 37 60 37 37]
[ 7 7 87 87 87 87]
[ 7 8 79 114 79 79]
[ 7 9 127 162 127 127]
[ 7 10 121 168 121 121]
[ 8 8 66 66 66 66]
[ 8 9 127 162 127 127]
[ 8 10 81 112 81 81]
[ 9 9 165 165 165 165]
[ 9 10 193 240 193 193]
[ 10 10 122 122 122 122]