COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.
COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA. COMPUTATIONAL PROBLEMS IN ABSTRACT ALGEBRA.
E TABLE 3. The X,, character block for odd classes of A not in A” Is 1, 28, 35, 84, 50, 350,300,567,210,840,700,175,1400,1050,1575, 1344,2100,2268,525,700,,972~4096,4200,2240,2835,6075,3200, 162 1 14 21 42 20 70 90 189 84 84 210 35 280 210 315 336 210 378 105 70 162 512 420 336 189 405 160 1225 l-2 5 10 4 -10 10 -3 4 20 18 3 -8 2 -21 16 -14 -6 -7 -10 18 0 4 16 -3 -21 32 122 2’ 1 2 1 2 0 2 -2 -3 0 4 2-5 o-2 7 0 -6 -6 -3 -6 6 0 -4 0 -3 9 0 144 1 6 9 10 0 10 10 29 16 -4 10 -5 0 -10 15 16 10 10 5 -10 -6 0 -20 -16 -19 -15 0 131 4 1 0 3 2-2 -4 0 1 2 0 -2 -1 0 -4 -3 O - 2 2 3 0 0 0 0 0 1 3 0 132 3 1 2 6 9 5 -5 0 9 9 -6 15 5 10 15 0 6 -15 -9 0 10 0 -16 0 6 9 0 -20 12123 l-2 2 1 1 -1 4 -3 1 2 3 -3 -2 -1 o-2 1 3-4 2 0 0 4 -2 -3 0 -4 132 3 1 4 4 1 - l 5 2 3 1 2 -3 1 -4 -1 0 -2 l-3 -2 2 0 0 2 2 3 0 0 134 1 0 0 1 3 l-2 -1 1 2 1 1 0 -1 o-2 11 2 2 0 0 -2 2-l 0 0 134 1 0 o-1 1 -1 0 1 -1 0 l-l o-1 0 0 l-10 00 0 0 0 10 0 4 2 32 l-l 0 3-l 1 0 0 -3 3 0 2 1 0 0 0 3 0 3 -5 0 -4 3 0 0 o-2 h 1*6 1 1 2 1 1 - 1 - 2 0 1 - 1 0 0 1 2 o - 2 1 0 -1 -1 0 0 l-2 0 0 2 2 913 l-l 0 o-1 1 0 0 0 00-l 10 0 0 000 10-l 0 0 0 0 1 a 2 33/P 1 5 3-3 2 7 9 O-6 3 3 -1 10 3 -9 -6 -6 0 6 -2 0 8 -3 -6 0 o-2 2 63/I 1 1 -1 1 -2 -1 1 o-2 -1 3 3 -2 -1 3 -2 -2 0 2 2 0 0 l-2 0 0 2 236/I21 -1 l-l 0 -1 1 0 0 l - 1 1 0 1 1 0 0 0 0 0 0 o-1 0 0 0 0 125 l-l 1 2 0 0 0 -1-1-1 0 0 0 0 0 1 o-2 0 o-1 2 0 1 -1 0 0 125 1 l-l 0 0 0 o-1 1 100 0 0 0 1000 o-1 0 o-1 1 0 0 2 3 5/P 1 2 l-l 0 0 o-1-1-1 0 0 0 0 0 1 0 1 0 0 0 -1 0 1 -1 0 0 2 7/I 1 0 0 o-1 o-1 0 0 000 0 0 0 0 0 0 0 0 1 1 0 0 0 -1 -1 224v l-2 1 10 8 2 2 -3 -8 -4 -6 -5 -16 14 -9 16 10 -6 13 14 18 0 -4 -16 -3 9 0 224u l-2 1 2 0 2 2 -3 0 -4 2 3 0 -2 -1 0 2 2 -3 -2 2 o-4 0 5 10 224 1 2 -3 2 4 -2 6 -3 4 -4 -6 3 8 -6 3 0 2-6 1 2 6 0 4 0 -3 -3 0 233v 1 1 -2 1 -1 -1 2 0 1 -1 0 -2 -1 2 o - 2 1 0 1 -1 0 o-1 2 0 0 0 116 l-l o-1 1 1 0 0 1-l 0 0 -1 0 0 o-1 0 l-10 0 10 0 0 0 8w 1 0 - 1 2 2 0 0 1 -2 o-2-1 0 0 1 0 -2 2 -1 0 0 0 0 0 1 -1 0 814 1 0 - 1 0 0 0 0 1 0 0 0 1 0 0 -1 0 0 o-1 0 0 0 0 o - 1 1 0 TABLE 4. The Z, W,, character block for even classes of F+. 8, 56, 160, 112, 840, 1296, 1400, 1008, 560,1400,, 4200, 400, 3240,4536,2400s 3360, 2800, 4096, 5600, 448, 448,1344,5600,2016,7168, 4 -4 16 24 4 -24 60 24 56 60 20 40 84 60 -80 16 -40 0 -80 32 -32 32 -80 48 0 2 -2 0 4 2 -4 -2 -4 4-2 2 4 2 -2 0 0 -4 0 0 0 0 0 8-8 0 4 12 16 8 20 24 -4 8 8 -4 4 -8 -12 12 16 -16 -24 0 -16 0 32 32 16 16 0 $j 2 2 0 o-2 o-2 0 o-2-2 0 2 2 0 0 0 0 0 0 0 0 0 0 0 m 5 11 34 31 21 81 95 90 74 - 25 -75 25 81 -81 60 -6 55 64 20 16 28 -60 -10 -90 -128 g 3-3 6 9 3-9 9 6 6 -15 3 -9 -9 9 -12 -18 9 0 12 0 -12 12 -6 -6 0 2 1 -1 -2 3 1 -3 3-6 2 3 -7 1 -3 3 4 -2 -1 0 4 8 4 -4 -2 6 0 2 1 -1 0 -1 1 1 -1 -2 2 -1 1 -1 l-l 0 0 10 0 0 0 o-2 2 0 2 1 3 -2 -1 5 -3 -1 2 2 -1 1 l-3 3 4 2 3 0 -4 0 -4 -4 -2 -2 0 cl 2 2 -2 4 -6 O-4 0 2 8 6 10 0 0 6 -6 10 -8 2-2 4 12 -4 0 -8 q 2-2 2 0 2 0 0 0 -2 0 -2 2 0 0 2 2 -2 0 2 -2 -4 4-4 0 0 s 2-l 1 1 0 0 -1 0 -1 2 o-2 0 0 0 0 1 1 -1 l-2 0 2 0 -2 m 1 l-l -1 0 0 1 0 1 1 o-1 0 0 0 0 -1 -1 1 -1 -1 0 1 0 -1 p 1 -2 2 -4 -3 0 4-9 7 13 -15 -4 0 0 3-12 8 8 -11 -16 2 6 -2 -18 32 c 3 6 6 0 3 0 0 -3 -3 3 3 0 0 o-3 0 0 0 3 0 6 -6 -6 -6 0 ; 1 o-2 2-l 0 2 -1 -1 -1 1 -2 0 0 1 2 0 o-1 0 2 2 -2 -2 0 2 4 16 20 -4 60 0 40 -36 -20 -20 -60 20 0 0 -60 60 80 -64 -20 - 16 44 60 100 36 -16 +$ 2 0 2 -2 -2 0 4 -2 -2 -2 2 2 0 0 2-2 0 0 -2 0 -2 -2 2 2 0 3 15 7-5 1 0 3 5 0 0 0 -5 -4 0 5 0 -4 0 -2 -2 -6 0 6 8 9 1 -1 -1 1 l-l 0 l-l 0 0 0 10 o-1 0 0 0 -2 2-2 0 2 0 0 l-l 1 1 1 0 O-l 0 0 0 1 -1 0 -1 o-1 0 l-2 0 0 0 2 2 4 O-2 O-6 0 2 0 0 0 0 O-6 0 0 0 4 0 2 2 6 0 4 2 1 -1 O-10 0 0 10 0 0 0 0 0 0 0 o-1 0 11 0 o-1 1 1 o-1 0 0 1 0 0 0 0 0 l-1 o-1 0 0 10 0 0 0 0 0 0
TABLE 5. The Z, character block for odd classes of F not in I;+. 18 21a35527 8, 56, 160, 112, 840, 1296, 1400, 1008, 560, 1400,, 4200, 400, 3240, 4536, 2400, 3360, 2800, 4096, 5600, 448, 162 210345 7 6 14 64 56 126 216 350 252 196 210 210 120 594 378 120 336 280 512 280 112 1223 21032 2-6 0 8 10 -24 10 -12 12 6-26 8 6 30 -24 -16 -24 0 8 16 122 22 283 2 2 0 0 2 0 -6 -4 4 -10 -2 0 6 6 8 0 0 O-8 0 144 203 5 4 4 16 16 4 16 20 24 24 -20 -20 0 -4 -20 O-16 0 0 0 0 1314 2s3 2-2 0 4 -2 -4 2 0 0 2 2 -4 -2 2 0 0 0 182 3 25335 3-l 4 11 -9 -9 5 0 16 15 15 15 9 -9 0 6 -: -1: -2: 4 4 l”12 3 2832 l-3 0 1 5 -3 -1 0 0 -3 5 1 3 -3 0 -2 3 0 4-4 9 182 3 2s32 3 3 6 3 3 3-3 0 0 3 3 -3 -3 3 0 o-3 0 0 0 % 134 263 1 l-2 1 1 l-l 0 0 1 1 3 -1 1 0 -4 3 0 0 0 5; 134 283 1 -1 0 -1 -1 1 1 0 0 -1 1 1 -1 1 0 o-1 0 0 0 8 2 32 2338 0 2-2 2 0 0 2 o-2 0 0 0 0 0 6 0 -2 -4 4 4 126 2332 2 0 0 2 -2 0 -2 0 0 0 -2 2 0 0 0 2 0 0 2 -2 2 913 2 32 0 -1 l-l 0 o-1 0 10 0 0 0 0 0 0 l-l 1 1 2 38113 243d 3 4 8-2 9 0 10 -9 -1 -3 -3 6 0 0 -3 6 8 -8 -1 -4 6 3/i 2&3% 1 0, 0 -2 -1 0 2 -3 3 3 -1 -2 0 0 3 -2 0 0 1 -4 2 3 b/I 2 233 1 -2 0 0 1 0 0 l-l 1 -1 0 0 0 1 0 0 o-1 0 125 2z3 5 1 -1-l 1 1 1 0 -3 1 0 0 0 -1 -2 0 1 0 2 0 2 125 22 5 1 l-l -1 l-l 0 1 1 0 0 0 -1 0 0 1 0 0 0 0 2 3 5/P 235 2 1 1 -1 -1 -1 0 0 -1 0 0 0 l - l 0 -1 0 1 0 1 2 7/I 27 1 o-1 0 0 10 0 0 0 o - 1 1 0 -1 0 0 -1 0 0
- Page 23 and 24: Some examples using coset enumerati
- Page 25 and 26: 40 C. M. Campbell Some examples usi
- Page 27 and 28: 44 N. S. Mendelsohn for example, in
- Page 29 and 30: 48 H. Jiirgensen Calculation with e
- Page 31 and 32: 52 H. Jiirgensen Calculation with e
- Page 33 and 34: 56 H. Jiirgensen Calculation with e
- Page 35 and 36: 60 V. Fe&h and J. Neubiiser 2. The
- Page 37 and 38: 64 L. Gerhards and E. Altmann Autom
- Page 39 and 40: 68 L. Gerhards and E. Altmann Autom
- Page 41 and 42: 72 L. Gerhards and E. Altmann ni E
- Page 43 and 44: 76 W. Lindenberg and L. Gerhards Se
- Page 45 and 46: 80 W. Lindenberg and L. Gerhards Se
- Page 47 and 48: 84 K. Ferber and H. Jiirgensen The
- Page 49 and 50: 7 The construction of the character
- Page 51 and 52: 92 John McKay defining multiplicati
- Page 53 and 54: 96 John McKay Construction of chara
- Page 55 and 56: 100 John McKay In the table, c indi
- Page 57 and 58: 104 C. Brott and J. Neubiiser irred
- Page 59 and 60: 108 C. Brott and J. Neubiiser eleme
- Page 61 and 62: 112 J. S. Frame The characters of t
- Page 63 and 64: 116 J. S. Frame 3. The decompositio
- Page 65 and 66: 120 J. S. Frame The characters of t
- Page 67: 124 J. S. Frame The characters of t
- Page 71 and 72: 132 R. Biilow and J. Neubiiser Deri
- Page 73 and 74: A search for simple groups of order
- Page 75 and 76: 140 Marshall Hall Jr. Simple groups
- Page 77 and 78: 144 Marshall Hall Jr. Simple groups
- Page 79 and 80: 148 Marshall Hall Jr. otherwise no
- Page 81 and 82: 152 Marshall Hall Jr. easily found
- Page 83 and 84: 156 Marshall Hall Jr. Simple groups
- Page 85 and 86: 160 Marshall Hail Jr. This leads to
- Page 87 and 88: 164 Marshall Hall Jr. b= (OO)(Ol, 0
- Page 89 and 90: 168 Marshall Hall Jr. 11. R. BRAUER
- Page 91 and 92: 172 Charles C. Sims THEOREM 2.3. Th
- Page 93 and 94: 176 Charles C. Sims has a set of im
- Page 95 and 96: 180 Degrc - No. Order t N (-63 Gene
- Page 97 and 98: An algorithm related to the restric
- Page 99 and 100: A module-theoretic computation rela
- Page 101 and 102: 192 A. L. Tritter expressed in the
- Page 103 and 104: 196 A. L. Tritter a question is mos
- Page 105 and 106: 200 John J. Cannon stack. The Cayle
- Page 107 and 108: , I The computation of irreducible
- Page 109 and 110: 208 P. G. Ruud and R. Keown product
- Page 111 and 112: 212 P. G. Ruud and R. Keown TX wher
- Page 113 and 114: 216 P. G. Ruud and R. Keown 4. L. G
- Page 115 and 116: 220 N. S. Mendelsohn where it is kn
- Page 117 and 118: 224 Robert J. Plemmons such class [
TABLE 5. The Z, character block for odd classes of F not in I;+.<br />
18 21a35527 8, 56, 160, 112, 840, 1296, 1400, 1008, 560, 1400,, 4200, 400, 3240, 4536, 2400, 3360, 2800, 4096, 5600, 448,<br />
162 210345 7 6 14 64 56 126 216 350 252 196 210 210 120 594 378 120 336 280 512 280 112<br />
1223 21032 2-6 0 8 10 -24 10 -12 12 6-26 8 6 30 -24 -16 -24 0 8 16<br />
122 22 283 2 2 0 0 2 0 -6 -4 4 -10 -2 0 6 6 8 0 0 O-8 0<br />
144 203 5 4 4 16 16 4 16 20 24 24 -20 -20 0 -4 -20 O-16 0 0 0 0<br />
1314 2s3 2-2 0 4 -2 -4 2 0 0 2 2 -4 -2 2 0 0 0<br />
182 3 25335 3-l 4 11 -9 -9 5 0 16 15 15 15 9 -9 0 6 -: -1: -2: 4 4<br />
l”12 3 2832 l-3 0 1 5 -3 -1 0 0 -3 5 1 3 -3 0 -2 3 0 4-4 9<br />
182 3 2s32 3 3 6 3 3 3-3 0 0 3 3 -3 -3 3 0 o-3 0 0 0 %<br />
134 263 1 l-2 1 1 l-l 0 0 1 1 3 -1 1 0 -4 3 0 0 0 5;<br />
134 283 1 -1 0 -1 -1 1 1 0 0 -1 1 1 -1 1 0 o-1 0 0 0 8<br />
2 32 2338 0 2-2 2 0 0 2 o-2 0 0 0 0 0 6 0 -2 -4 4 4<br />
126 2332 2 0 0 2 -2 0 -2 0 0 0 -2 2 0 0 0 2 0 0 2 -2<br />
2 913 2 32 0 -1 l-l 0 o-1 0 10 0 0 0 0 0 0 l-l 1 1<br />
2 38113 243d 3 4 8-2 9 0 10 -9 -1 -3 -3 6 0 0 -3 6 8 -8 -1 -4<br />
6 3/i 2&3% 1 0, 0 -2 -1 0 2 -3 3 3 -1 -2 0 0 3 -2 0 0 1 -4<br />
2 3 b/I 2 233 1 -2 0 0 1 0 0 l-l 1 -1 0 0 0 1 0 0 o-1 0<br />
125 2z3 5 1 -1-l 1 1 1 0 -3 1 0 0 0 -1 -2 0 1 0 2 0 2<br />
125 22 5 1 l-l -1 l-l 0 1 1 0 0 0 -1 0 0 1 0 0 0 0<br />
2 3 5/P 235 2 1 1 -1 -1 -1 0 0 -1 0 0 0 l - l 0 -1 0 1 0 1<br />
2 7/I 27 1 o-1 0 0 10 0 0 0 o - 1 1 0 -1 0 0 -1 0 0
Change language