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Alperin–Brauer–Gorenstein theorem

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279: 231: 159: 76: 320: 259: 339: 313: 41: 344: 37: 306: 168: 215: 82:
proved this in the course of 261 pages. The subdivision by 2-fusion is sketched there, given as an exercise in
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of odd order, depending on a certain congruence, or to the
294: 79: 57: 232:"On finite groups with quasidihedral Sylow 2-groups" 36:. These are isomorphic either to three-dimensional 70: 160:Transactions of the American Mathematical Society 87: 314: 230:Kwon, T.; Lee, K.; Cho, I.; Park, S. (1980), 8: 321: 307: 236:Journal of the Korean Mathematical Society 86:, Ch. 7), and presented in some detail in 83: 125:of the same order, that is, if it is the 62: 56: 98: 80:Alperin, Brauer & Gorenstein (1970) 7: 275: 273: 14: 42:projective special unitary groups 22:Alperin–Brauer–Gorenstein theorem 277: 38:projective special linear groups 1: 169:American Mathematical Society 129:of a cyclic 2-group with the 340:Theorems about finite groups 293:. You can help Knowledge by 216:Harper & Row Publishers 361: 272: 24:characterizes the finite 345:Abstract algebra stubs 289:-related article is a 109:if it is a nonabelian 72: 71:{\displaystyle M_{11}} 73: 55: 111:semidirect product 88:Kwon et al. (1980) 68: 302: 301: 34:Sylow 2-subgroups 352: 323: 316: 309: 287:abstract algebra 281: 274: 269: 268: 267: 258:, archived from 226: 203: 134: 115:maximal subgroup 103: 84:Gorenstein (1968 77: 75: 74: 69: 67: 66: 360: 359: 355: 354: 353: 351: 350: 349: 330: 329: 328: 327: 265: 263: 229: 206: 177:10.2307/1995627 145: 142: 137: 131:symmetric group 104: 100: 96: 58: 53: 52: 12: 11: 5: 358: 356: 348: 347: 342: 332: 331: 326: 325: 318: 311: 303: 300: 299: 282: 271: 270: 227: 208:Gorenstein, D. 204: 155:Gorenstein, D. 147:Alperin, J. L. 141: 138: 136: 135: 127:wreath product 119:direct product 97: 95: 92: 65: 61: 13: 10: 9: 6: 4: 3: 2: 357: 346: 343: 341: 338: 337: 335: 324: 319: 317: 312: 310: 305: 304: 298: 296: 292: 288: 283: 280: 276: 262:on 2011-07-22 261: 257: 253: 249: 245: 241: 237: 233: 228: 225: 221: 217: 213: 212:Finite groups 209: 205: 202: 198: 194: 190: 186: 182: 178: 174: 170: 166: 162: 161: 156: 152: 148: 144: 143: 139: 132: 128: 124: 123:cyclic groups 120: 116: 112: 108: 105:A 2-group is 102: 99: 93: 91: 89: 85: 81: 63: 59: 51: 50:Mathieu group 47: 43: 39: 35: 31: 30:quasidihedral 27: 26:simple groups 23: 19: 295:expanding it 284: 264:, retrieved 260:the original 242:(1): 91–97, 239: 235: 211: 164: 158: 133:on 2 points. 106: 101: 46:finite field 32:or wreathed 21: 15: 18:mathematics 334:Categories 266:2010-07-16 151:Brauer, R. 140:References 117:that is a 248:0304-9914 185:0002-9947 171:: 1–261, 210:(1968), 107:wreathed 256:0593804 224:0231903 201:0284499 193:1995627 121:of two 44:over a 254:  246:  222:  199:  191:  183:  20:, the 285:This 189:JSTOR 167:(1), 113:of a 94:Notes 28:with 291:stub 244:ISSN 181:ISSN 173:doi 165:151 78:. 40:or 16:In 336:: 252:MR 250:, 240:17 238:, 234:, 220:MR 218:, 214:, 197:MR 195:, 187:, 179:, 163:, 153:; 149:; 90:. 64:11 322:e 315:t 308:v 297:. 175:: 60:M

Index

mathematics
simple groups
quasidihedral
Sylow 2-subgroups
projective special linear groups
projective special unitary groups
finite field
Mathieu group
Alperin, Brauer & Gorenstein (1970)
Gorenstein (1968
Kwon et al. (1980)
semidirect product
maximal subgroup
direct product
cyclic groups
wreath product
symmetric group
Alperin, J. L.
Brauer, R.
Gorenstein, D.
Transactions of the American Mathematical Society
American Mathematical Society
doi
10.2307/1995627
ISSN
0002-9947
JSTOR
1995627
MR
0284499

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