Subgroup Growth

Copertina anteriore
Springer Science & Business Media, 1 apr 2003 - 454 pagine

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2001.

Subgroup growth studies the distribution of subgroups of finite index in a group as a function of the index. In the last two decades this topic has developed into one of the most active areas of research in infinite group theory; this book is a systematic and comprehensive account of the substantial theory which has emerged.
As well as determining the range of possible 'growth types', for finitely generated groups in general and for groups in particular classes such as linear groups, a main focus of the book is on the tight connection between the subgroup growth of a group and its algebraic structure.
A wide range of mathematical disciplines play a significant role in this work: as well as various aspects of infinite group theory, these include finite simple groups and permutation groups, profinite groups, arithmetic groups and Strong Approximation, algebraic and analytic number theory, probability, and p-adic model theory. Relevant aspects of such topics are explained in self-contained 'windows'.

 

Sommario

III
1
IV
2
V
3
VI
8
VII
9
IX
11
X
12
XI
13
XCI
217
XCIII
223
XCIV
224
XCV
227
XCVI
228
XCVII
231
XCVIII
232
XCIX
234

XII
14
XIII
20
XIV
22
XV
24
XVI
26
XVII
28
XVIII
29
XIX
31
XX
34
XXI
36
XXII
36
XXIII
37
XXIV
40
XXV
41
XXVI
48
XXVII
49
XXIX
53
XXX
56
XXXI
59
XXXII
61
XXXIII
67
XXXIV
70
XXXV
71
XXXVII
72
XXXVIII
75
XXXIX
78
XL
81
XLI
84
XLIII
88
XLIV
89
XLVI
92
XLVII
94
XLVIII
96
XLIX
99
L
100
LI
102
LII
106
LIII
109
LIV
113
LV
119
LVI
123
LVII
126
LVIII
130
LIX
131
LXI
134
LXII
139
LXIII
147
LXIV
149
LXV
151
LXVI
154
LXVII
156
LXVIII
158
LXIX
159
LXX
160
LXXI
162
LXXII
165
LXXIII
170
LXXIV
173
LXXV
175
LXXVII
178
LXXVIII
179
LXXIX
185
LXXX
192
LXXXI
195
LXXXII
198
LXXXIII
199
LXXXV
203
LXXXVI
205
LXXXVII
207
LXXXVIII
209
LXXXIX
212
XC
215
C
235
CI
239
CII
241
CIV
242
CV
246
CVI
253
CVII
258
CVIII
264
CIX
267
CXI
269
CXII
272
CXIII
275
CXIV
281
CXV
283
CXVII
288
CXVIII
295
CXIX
302
CXX
305
CXXI
307
CXXIII
310
CXXIV
311
CXXV
313
CXXVI
316
CXXVII
317
CXXX
318
CXXXI
320
CXXXIII
321
CXXXV
322
CXXXVI
323
CXXXVII
327
CXXXVIII
329
CXXXIX
330
CXLI
332
CXLII
333
CXLIV
335
CXLVI
336
CXLVII
341
CXLVIII
347
CL
350
CLI
351
CLII
355
CLIV
357
CLV
359
CLVI
361
CLVII
362
CLVIII
365
CLXI
367
CLXII
370
CLXIII
373
CLXVI
374
CLXVIII
375
CLXIX
377
CLXXII
381
CLXXIII
383
CLXXIV
387
CLXXVI
395
CLXXVII
398
CLXXVIII
404
CLXXIX
407
CLXXXI
409
CLXXXII
411
CLXXXIII
413
CLXXXV
417
CLXXXVIII
419
CLXXXIX
423
CXCII
426
CXCIV
427
CXCVII
428
CXCIX
429
CC
431
CCI
444
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