470:
Finite simple groups. Proceedings of an
Instructional Conference organized by the London Mathematical Society (a NATO Advanced Study Institute), Oxford, September 1969
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481:
71:
552:
119:
284:
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Guralnick, Robert M.; Robinson, Geoffrey R. (1993), "On extensions of the Baer-Suzuki theorem",
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464:(1971), "Character theory pertaining to finite simple groups", in Powell, M. B.;
461:
75:
48:
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122:(and the proof uses the BrauerâSuzuki theorem to deal with some small cases).
681:
662:
573:
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36:
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have also studied an extension of the Z* theorem to pairs of groups (
614:
428:, which also contains several useful results in the finite case.
398:
414:
598:"Centralizers of normal subgroups and the Z*-theorem"
495:
gives a detailed proof of the BrauerâSuzuki theorem.
134:
gave several criteria for an element to lie outside
420:. This was also generalized to odd primes and to
549:
382:
679:
596:Henke, Ellen; Semeraro, Jason (1 October 2015).
502:(1966), "Central elements in core-free groups",
632:
425:
595:
431:
498:
131:
652:
633:Mislin, Guido; Thévenaz, Jacques (1991),
623:
613:
517:
635:"The Z*-theorem for compact Lie groups"
680:
330:A simple corollary is that an element
188:satisfying the following properties:
157:, it is necessary and sufficient for
460:
13:
14:
699:
94:), which is the inverse image in
383:Guralnick & Robinson (1993)
346:) if and only if there is some
625:10.1016/j.jalgebra.2015.06.027
453:
86:, then the involution lies in
1:
553:Israel Journal of Mathematics
389:is an element of prime order
688:Theorems about finite groups
519:10.1016/0021-8693(66)90030-5
426:Mislin & Thévenaz (1991)
7:
432:Henke & Semeraro (2015)
10:
704:
125:
377:A generalization to odd
82:to any other element of
413:is central modulo the
328:
306:may be chosen to have
145:Its theorem 4 states:
116:
24:is stated as follows:
640:Mathematische Annalen
446:a normal subgroup of
169:) that there is some
147:
120:BrauerâSuzuki theorem
118:This generalizes the
26:
476:, pp. 249â327,
314:is in the center of
273:is generated by the
47:) being its maximal
130:The original paper
654:10.1007/BF01445193
602:Journal of Algebra
566:10.1007/BF02808114
505:Journal of Algebra
500:Glauberman, George
422:compact Lie groups
483:978-0-12-563850-0
322:may be chosen in
132:Glauberman (1966)
18:George Glauberman
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673:
656:
629:
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617:
592:
546:
521:
494:
462:Dade, Everett C.
381:was recorded in
291:is equal to the
256:is contained in
217:is contained in
195:normalizes both
179:abelian subgroup
144:
64:Sylow 2-subgroup
16:In mathematics,
703:
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693:
692:
678:
677:
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277:-conjugates of
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161:to lie outside
149:For an element
135:
128:
49:normal subgroup
12:
11:
5:
701:
691:
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675:
674:
647:(1): 103â111,
630:
593:
560:(1): 281â297,
547:
512:(3): 403â420,
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474:Academic Press
472:, Boston, MA:
466:Higman, Graham
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70:containing an
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374:-conjugate.
371:
367:
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362:commute and
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44:
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37:finite group
32:
28:
27:
21:
15:
608:: 511â514.
454:Works cited
308:prime power
213:), that is
201:centralizer
29:Z* theorem:
590:0794.20029
544:0145.02802
397:has order
395:commutator
354:such that
338:is not in
326:otherwise.
72:involution
22:Z* theorem
663:0025-5831
615:1411.1932
574:0021-2172
528:0021-8693
438:,
310:order if
302:Moreover
76:conjugate
682:Category
468:(eds.),
405:for all
393:and the
285:exponent
199:and the
671:1125010
582:1239051
536:0202822
492:0360785
442:) with
409:, then
399:coprime
126:Details
98:of the
39:, with
669:
661:
588:
580:
572:
542:
534:
526:
490:
480:
418:âČ-core
379:primes
318:, and
100:center
58:. If
610:arXiv
385:: if
293:order
62:is a
56:order
35:be a
659:ISSN
570:ISSN
524:ISSN
478:ISBN
370:are
366:and
358:and
283:the
260:and
232:) â©
177:and
74:not
31:Let
649:doi
645:291
620:doi
606:439
586:Zbl
562:doi
540:Zbl
514:doi
424:in
401:to
334:in
295:of
287:of
184:of
173:in
153:in
102:of
78:in
66:of
53:odd
51:of
20:'s
684::
667:MR
665:,
657:,
643:,
637:,
618:.
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600:.
584:,
578:MR
576:,
568:,
558:82
556:,
538:,
532:MR
530:,
522:,
508:,
488:MR
486:,
450:.
350:â
340:Z*
266:gt
264:â
262:tg
250:))
221:=
163:Z*
143:).
137:Z*
114:).
88:Z*
651::
628:.
622::
612::
564::
516::
510:4
448:G
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440:H
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387:t
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368:t
364:s
360:t
356:s
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348:s
344:G
342:(
336:T
332:t
324:T
320:g
316:T
312:t
304:g
297:t
289:U
279:t
275:N
271:U
258:U
254:t
248:U
246:(
243:T
241:C
239:(
236:G
234:N
230:U
228:(
225:G
223:N
219:N
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211:U
209:(
206:T
204:C
197:U
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186:T
182:U
175:G
171:g
167:G
165:(
159:t
155:T
151:t
141:G
139:(
112:G
110:(
108:O
106:/
104:G
96:G
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90:(
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33:G
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