Characters of Finite Groups. Part 1

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American Mathematical Soc., Dec 2, 1997 - Characters of groups
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This book discusses character theory and its applications to finite groups. The work places the subject within the reach of people with a relatively modest mathematical background. The necessary background exceeds the standard algebra course with respect only to finite groups. Starting with basic notions and theorems in character theory, the authors present a variety of results on the properties of complex-valued characters and applications to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations and applications of monomial groups. The presentation is detailed, and many proofs of known results are new. Most of the results in the book are presented in monograph form for the first time. Numerous exercises offer additional information on the topics and help readers to understand the main concepts and results.
 

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Characters of finite groups

Contents

III
1
IV
3
V
4
VI
6
VII
7
VIII
9
IX
10
X
11
LXVI
171
LXVII
172
LXVIII
174
LXIX
176
LXX
183
LXXI
185
LXXII
187
LXXIII
189

XI
13
XII
17
XIII
23
XVI
25
XVII
27
XVIII
29
XIX
31
XX
36
XXI
37
XXII
38
XXIII
43
XXV
45
XXVI
47
XXVII
48
XXIX
50
XXX
53
XXXI
55
XXXII
57
XXXIII
59
XXXIV
62
XXXV
66
XXXVI
67
XXXVII
71
XXXVIII
74
XXXIX
77
XL
78
XLI
83
XLII
84
XLIII
90
XLIV
92
XLV
94
XLVI
103
XLVII
106
XLVIII
107
XLIX
109
L
116
LI
118
LII
120
LIII
121
LIV
125
LV
126
LVI
127
LVII
136
LVIII
137
LIX
141
LX
143
LXI
144
LXII
152
LXIII
156
LXIV
163
LXV
170
LXXIV
196
LXXV
199
LXXVI
200
LXXVII
205
LXXVIII
207
LXXIX
211
LXXX
213
LXXXI
214
LXXXII
215
LXXXIII
216
LXXXIV
217
LXXXVI
219
LXXXVII
220
LXXXVIII
225
XC
229
XCI
230
XCII
231
XCIII
232
XCIV
238
XCV
241
XCVI
250
XCVII
257
XCVIII
263
XCIX
267
C
274
CI
279
CII
289
CIII
299
CIV
300
CV
303
CVI
314
CVII
315
CVIII
318
CIX
327
CX
331
CXI
334
CXII
335
CXIII
336
CXIV
337
CXV
339
CXVI
342
CXVII
343
CXVIII
344
CXIX
345
CXX
351
CXXI
353
CXXII
357
CXXIII
361
CXXIV
377
CXXV
379
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