177:
Feit proved several theorems giving conditions under which a set of characters is coherent. A typical one is as follows. Suppose that
492:
165:) is non-zero. Although strictly speaking coherence is really a property of the isometry Ď„, it is common to say that the set
32:
from the degree-zero subspace of a space of characters to the whole space. The general notion of coherence was developed by
548:
481:
1960 Institute on Finite Groups: Held at
California Institute of Technology, Pasadena, California, August 1-August 28, 1960
523:
603:
344:
is the Sylow 2-subgroup and Ď„ is induction, then coherence fails for the second reason. The abelianization of
484:
410:
57:
598:
476:
403:
85:
49:
44:), as a generalization of the proof by Frobenius of the existence of a Frobenius kernel of a
17:
582:
533:
502:
465:
364:
In the proof of the
Frobenius theory about the existence of a kernel of a Frobenius group
8:
61:
314:
570:
519:
488:
453:
409:
In more complicated cases the isometry Ď„ is no longer induction. For example, in the
309:
is a Sylow 2-subgroup, with Ď„ induction, then coherence fails for the first reason:
560:
544:
443:
25:
578:
529:
513:
498:
461:
431:
45:
592:
574:
457:
448:
414:
565:
540:
509:
472:
427:
33:
186:
243:
acts simply transitively on its non-identity elements (in which case
29:
56:, Chapter 3) developed coherence further in the proof of the
483:, Proc. Sympos. Pure Math., vol. VI, Providence, R.I.:
212:
in their kernel. Suppose that Ď„ is a linear isometry from
332:
is the simple Suzuki group of order (2–1) 2( 2+1) with
432:"On a class of doubly transitive permutation groups"
325:has order 2–1 and acts simply transitively on it.
169:is coherent instead of saying that Ď„ is coherent.
100:) for the set of integral linear combinations of
590:
391:) is just induction, although its extension to
539:
518:, W. A. Benjamin, Inc., New York-Amsterdam,
376:is the set of all irreducible characters of
53:
477:"Group characters. Exceptional characters"
142:if it can be extended to an isometry from
564:
447:
269:whose abelianization has order at most 4|
115:) for the subset of degree 0 elements of
134:) to the degree 0 virtual characters of
48:and of the work of Brauer and Suzuki on
591:
123:). Suppose that Ď„ is an isometry from
549:"Solvability of groups of odd order"
508:
471:
426:
41:
37:
406:the isometry Ď„ is again induction.
372:is the subgroup fixing a point and
235:is an elementary abelian group and
13:
223:) into the degree 0 characters of
14:
615:
204:be the irreducible characters of
196:is a Frobenius group with kernel
172:
76:is a subgroup of a finite group
436:Illinois Journal of Mathematics
553:Pacific Journal of Mathematics
1:
485:American Mathematical Society
420:
359:
348:has order 2, while the group
227:. Then Ď„ is coherent unless
67:
28:that allows one to extend an
7:
515:Characters of finite groups
479:, in Hall, Marshall (ed.),
402:Similarly in the theory of
281:
64:of odd order are solvable.
10:
620:
181:is a subgroup of a group
54:Feit & Thompson (1963
24:is a property of sets of
566:10.2140/pjm.1963.13.775
449:10.1215/ijm/1255455862
413:the isometry Ď„ is the
404:exceptional characters
290:is the simple group SL
265:-group for some prime
86:irreducible characters
50:exceptional characters
604:Representation theory
411:Feit–Thompson theorem
58:Feit–Thompson theorem
18:representation theory
399:) is not induction.
380:, the isometry Ď„ on
368:where the subgroup
150:) to characters of
138:. Then Ď„ is called
487:, pp. 67–70,
315:elementary abelian
545:Thompson, John G.
494:978-0-8218-1406-2
261:is a non-abelian
208:that do not have
611:
585:
568:
536:
505:
468:
451:
16:In mathematical
619:
618:
614:
613:
612:
610:
609:
608:
589:
588:
526:
495:
423:
386:
362:
356:has order 2–1.
300:
293:
284:
249:
218:
175:
160:
129:
110:
70:
46:Frobenius group
12:
11:
5:
617:
607:
606:
601:
587:
586:
537:
524:
506:
493:
469:
442:(2): 170–186,
422:
419:
384:
361:
358:
298:
291:
283:
280:
279:
278:
255:
247:
216:
174:
173:Feit's theorem
171:
158:
127:
108:
69:
66:
9:
6:
4:
3:
2:
616:
605:
602:
600:
599:Finite groups
597:
596:
594:
584:
580:
576:
572:
567:
562:
558:
554:
550:
546:
542:
538:
535:
531:
527:
525:9780805324341
521:
517:
516:
511:
507:
504:
500:
496:
490:
486:
482:
478:
474:
470:
467:
463:
459:
455:
450:
445:
441:
437:
433:
429:
425:
424:
418:
416:
415:Dade isometry
412:
407:
405:
400:
398:
394:
390:
383:
379:
375:
371:
367:
357:
355:
351:
347:
343:
339:
335:
331:
326:
324:
320:
316:
312:
308:
304:
297:
289:
276:
272:
268:
264:
260:
256:
253:
246:
242:
238:
234:
230:
229:
228:
226:
222:
215:
211:
207:
203:
199:
195:
191:
188:
184:
180:
170:
168:
164:
157:
153:
149:
145:
141:
137:
133:
126:
122:
118:
114:
107:
103:
99:
95:
91:
87:
83:
79:
75:
72:Suppose that
65:
63:
59:
55:
51:
47:
43:
39:
35:
31:
27:
23:
19:
559:: 775–1029,
556:
552:
541:Feit, Walter
514:
510:Feit, Walter
480:
473:Feit, Walter
439:
435:
428:Feit, Walter
408:
401:
396:
392:
388:
381:
377:
373:
369:
365:
363:
353:
349:
345:
341:
337:
333:
329:
327:
322:
318:
310:
306:
302:
295:
287:
285:
274:
270:
266:
262:
258:
251:
244:
240:
236:
232:
224:
220:
213:
209:
205:
201:
197:
193:
192:, such that
189:
182:
178:
176:
166:
162:
155:
151:
147:
143:
139:
135:
131:
124:
120:
116:
112:
105:
101:
97:
93:
89:
81:
77:
73:
71:
21:
15:
593:Categories
421:References
340:>1 and
305:>1 and
254:) is zero)
200:, and let
187:normalizer
68:Definition
26:characters
575:0030-8730
458:0019-2082
84:a set of
60:that all
22:coherence
547:(1963),
512:(1967),
475:(1962),
430:(1960),
360:Examples
336:odd and
282:Examples
140:coherent
92:. Write
30:isometry
583:0166261
534:0219636
503:0132779
466:0113953
231:either
36: (
581:
573:
532:
522:
501:
491:
464:
456:
301:) for
104:, and
80:, and
62:groups
185:with
571:ISSN
520:ISBN
489:ISBN
454:ISSN
317:and
277:|+1.
154:and
42:1962
38:1960
34:Feit
561:doi
444:doi
328:If
313:is
286:If
257:or
88:of
595::
579:MR
577:,
569:,
557:13
555:,
551:,
543:;
530:MR
528:,
499:MR
497:,
462:MR
460:,
452:,
438:,
434:,
417:.
52:.
40:,
20:,
563::
446::
440:4
397:S
395:(
393:I
389:S
387:(
385:0
382:I
378:H
374:S
370:H
366:G
354:H
352:/
350:N
346:H
342:H
338:n
334:n
330:G
323:H
321:/
319:N
311:H
307:H
303:n
299:2
296:F
294:(
292:2
288:G
275:H
273:/
271:N
267:p
263:p
259:H
252:S
250:(
248:0
245:I
241:H
239:/
237:N
233:H
225:G
221:S
219:(
217:0
214:I
210:H
206:N
202:S
198:H
194:N
190:N
183:G
179:H
167:S
163:S
161:(
159:0
156:I
152:G
148:S
146:(
144:I
136:G
132:S
130:(
128:0
125:I
121:S
119:(
117:I
113:S
111:(
109:0
106:I
102:S
98:S
96:(
94:I
90:H
82:S
78:G
74:H
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