Knowledge (XXG)

ZJ theorem

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You can help Knowledge (XXG) by 183:is the maximal normal subgroup of 14: 634: 143:: the subgroup generated by the 521:Canadian Journal of Mathematics 351:, and = 1, then the image of 1: 697:Theorems about finite groups 607:10.1016/0021-8693(69)90068-4 375:) is contained in a normal 718: 629: 252:) is the maximal normal 117:Notation and definitions 702:Abstract algebra stubs 646:-related article is a 535:10.4153/cjm-1968-107-2 215:is the maximal normal 565:, New York: Chelsea, 426:) ≠ 1 is said to be 309:) ≠ 1 is said to be 257:-nilpotent subgroup 593:Journal of Algebra 512:Glauberman, George 449:) is contained in 659: 658: 588:Thompson, John G. 572:978-0-8284-0301-6 405:For an odd prime 288:For an odd prime 145:abelian subgroups 132:Thompson subgroup 39:-constrained and 28:states that if a 22:George Glauberman 709: 680: 673: 666: 644:abstract algebra 638: 631: 626: 609: 583: 554: 537: 489: 479: 458: 381: 340: 328: 269: 241: 201: 180: 75: 717: 716: 712: 711: 710: 708: 707: 706: 687: 686: 685: 684: 586: 573: 557: 510: 507: 495: 487: 474: 464: 456: 444: 421: 397: 387: 376: 370: 360: 347:) is normal in 341: 338: 323: 304: 267: 247: 239: 214: 199: 182: 178: 119: 94:)) is a normal 77: 73: 12: 11: 5: 715: 713: 705: 704: 699: 689: 688: 683: 682: 675: 668: 660: 657: 656: 639: 628: 627: 600:(2): 149–151, 584: 571: 559:Gorenstein, D. 555: 506: 503: 502: 501: 484: 453: 440: 417: 403: 393: 383: 366: 356: 336: 300: 286: 277:, part of the 236: 231: 210: 205: 175: 170: 152: 118: 115: 70: 13: 10: 9: 6: 4: 3: 2: 714: 703: 700: 698: 695: 694: 692: 681: 676: 674: 669: 667: 662: 661: 655: 653: 649: 645: 640: 637: 633: 625: 621: 617: 613: 608: 603: 599: 595: 594: 589: 585: 582: 578: 574: 568: 564: 563:Finite Groups 560: 556: 553: 549: 545: 541: 536: 531: 528:: 1101–1135, 527: 523: 522: 517: 513: 509: 508: 504: 499: 494: 490: 483: 477: 472: 468: 463: 459: 452: 448: 443: 438: 434: 433: 431: 425: 420: 416: 412: 408: 404: 401: 396: 391: 386: 379: 374: 369: 364: 359: 354: 350: 346: 342: 332: 326: 321: 317: 316: 314: 308: 303: 299: 295: 291: 287: 284: 282: 276: 274: 270: 262: 258: 256: 251: 246: 242: 235: 232: 229: 227: 222: 219:-subgroup of 218: 213: 209: 206: 204: 202: 194: 190: 186: 181: 174: 171: 168: 164: 160: 156: 153: 150: 146: 142: 138: 134: 133: 128: 124: 121: 120: 116: 114: 112: 109: 107: 101: 97: 93: 89: 85: 81: 76: 69: 65: 62: 59: 55: 53: 49: 45: 43: 38: 34: 31: 27: 23: 19: 652:expanding it 641: 597: 591: 562: 525: 519: 497: 492: 485: 481: 475: 470: 466: 461: 454: 450: 446: 441: 432:-constrained 429: 427: 423: 418: 414: 410: 406: 399: 394: 389: 384: 377: 372: 367: 362: 357: 352: 348: 344: 334: 330: 324: 319: 318:if whenever 312: 310: 306: 301: 297: 293: 289: 280: 272: 265: 260: 254: 249: 244: 237: 233: 225: 220: 216: 211: 207: 197: 192: 184: 176: 172: 166: 161:) means the 158: 154: 140: 136: 130: 126: 122: 110: 105: 99: 91: 87: 83: 79: 71: 67: 63: 51: 41: 36: 32: 30:finite group 25: 15: 473:is a Sylow 469:) whenever 437:centralizer 165:of a group 147:of maximal 18:mathematics 691:Categories 505:References 409:, a group 333:such that 292:, a group 102:, for any 46:and has a 26:ZJ theorem 616:0021-8693 544:0008-414X 478:-subgroup 380:-subgroup 327:-subgroup 187:of order 129:) is the 108:-subgroup 56:for some 54:-subgroup 561:(1980), 514:(1968), 96:subgroup 624:0245683 581:0569209 552:0230807 435:if the 315:-stable 283:-series 189:coprime 139:-group 66:, then 44:-stable 622:  614:  579:  569:  550:  542:  279:upper 263:, the 223:, the 195:, the 163:center 104:Sylow 48:normal 642:This 413:with 322:is a 296:with 275:-core 228:-core 203:-core 149:order 135:of a 61:prime 648:stub 612:ISSN 567:ISBN 540:ISSN 382:of N 355:in N 602:doi 530:doi 480:of 392:)/C 365:)/C 329:of 259:of 191:to 98:of 58:odd 35:is 24:'s 16:In 693:: 620:MR 618:, 610:, 598:13 596:, 577:MR 575:, 548:MR 546:, 538:, 526:20 524:, 518:, 500:). 402:). 335:PO 113:. 20:, 679:e 672:t 665:v 654:. 604:: 532:: 498:G 496:( 493:p 491:, 488:′ 486:p 482:O 476:p 471:P 467:G 465:( 462:p 460:, 457:′ 455:p 451:O 447:P 445:( 442:G 439:C 430:p 424:G 422:( 419:p 415:O 411:G 407:p 400:P 398:( 395:G 390:P 388:( 385:G 378:p 373:P 371:( 368:G 363:P 361:( 358:G 353:x 349:G 345:G 343:( 339:′ 337:p 331:G 325:p 320:P 313:p 307:G 305:( 302:p 298:O 294:G 290:p 285:. 281:p 273:p 271:, 268:′ 266:p 261:G 255:p 250:G 248:( 245:p 243:, 240:′ 238:p 234:O 230:. 226:p 221:G 217:p 212:p 208:O 200:′ 198:p 193:p 185:G 179:′ 177:p 173:O 169:. 167:H 159:H 157:( 155:Z 151:. 141:S 137:p 127:S 125:( 123:J 111:S 106:p 100:G 92:S 90:( 88:J 86:( 84:Z 82:) 80:G 78:( 74:′ 72:p 68:O 64:p 52:p 42:p 37:p 33:G

Index

mathematics
George Glauberman
finite group
p-stable
normal
p-subgroup
odd
prime
subgroup
Sylow p-subgroup
Thompson subgroup
abelian subgroups
order
center
coprime
p-core
p-core
p-nilpotent subgroup
p,p-core
upper p-series
p-stable
p-constrained
centralizer
Glauberman, George
"A characteristic subgroup of a p-stable group"
Canadian Journal of Mathematics
doi
10.4153/cjm-1968-107-2
ISSN
0008-414X

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