Subgroup growth:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Deutsch |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
2003
|
| Schriftenreihe: | Progress in mathematics
212 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXII, 453 S. 940 gr. |
| ISBN: | 3764369892 |
Internformat
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| 245 | 1 | 0 | |a Subgroup growth |c Alexander Lubotzky ; Dan Segal |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2003 | |
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| 490 | 1 | |a Progress in mathematics |v 212 | |
| 650 | 4 | |a Croissance de sous-groupes (Mathématiques) | |
| 650 | 4 | |a Groupes infinis | |
| 650 | 7 | |a Teoria dos grupos |2 larpcal | |
| 650 | 7 | |a Álgebra |2 larpcal | |
| 650 | 4 | |a Infinite groups | |
| 650 | 4 | |a Subgroup growth (Mathematics) | |
| 650 | 0 | 7 | |a Asymptotik |0 (DE-588)4126634-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Untergruppe |0 (DE-588)4224972-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 2 | |a Asymptotik |0 (DE-588)4126634-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Segal, Daniel |d 1947- |e Verfasser |0 (DE-588)133203670 |4 aut | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010441681 | |
Datensatz im Suchindex
| _version_ | 1819381865458434048 |
|---|---|
| adam_text | Contents
Preface xv
Notation xxi
0 Introduction and Overview 1
0.1 Preliminary comments and definitions 2
0.2 Overview of the chapters 3
0.3 On CFSG 8
0.4 The windows 9
0.5 The notes 9
1 Basic Techniques of Subgroup Counting 11
1.1 Permutation representations 12
1.2 Quotients and subgroups 13
1.3 Group extensions 14
1.4 Nilpotent and soluble groups 20
1.5 Abelian groups I 22
1.6 Finite p groups 24
1.7 Sylow s theorem 26
1.8 Restricting to soluble subgroups 28
1.9 Applications of the minimal index 29
1.10 Abelian groups II 31
1.11 Growth types 34
Notes 36
2 Free Groups 37
2.1 The subgroup growth of free groups 39
2.2 Subnormal subgroups 42
2.3 Counting d generator finite groups 43
Notes 50
3 Groups with Exponential Subgroup Growth 51
3.1 Upper bounds 55
3.2 Lower bounds 58
3.3 Free pro p groups 61
x Contents
3.4 Normal subgroups in free pro p groups 63
3.5 Relations in p groups and Lie algebras 69
Notes 72
4 Pro p Groups 73
4.1 Pro p groups with polynomial subgroup growth 74
4.2 Pro p groups with slow subgroup growth 77
4.3 The groups SL^(Fp[[t]]) 80
4.4 A perfect groups 83
4.5 The Nottingham group 86
4.6 Finitely presented pro p groups 86
Notes 90
5 Finitely Generated Groups with Polynomial Subgroup Growth ... 91
5.1 Preliminary observations 94
5.2 Linear groups with PSG 96
5.3 Upper chief factors 98
5.4 Groups of prosoluble type 101
5.5 Groups of finite upper rank 102
5.6 The degree of polynomial subgroup growth 104
Notes 108
6 Congruence Subgroups Ill
6.1 The characteristic 0 case 115
6.2 The positive characteristic case 121
6.3 Perfect Lie algebras 125
6.4 Normal congruence subgroups 128
Notes 132
7 The Generalized Congruence Subgroup Problem 133
7.1 The congruence subgroup problem 136
7.2 Subgroup growth of lattices 141
7.3 Counting hyperbolic manifolds 149
Notes 151
8 Linear Groups 153
8.1 Subgroup growth, characteristic 0 155
8.2 Residually nilpotent groups 156
8.3 Subgroup growth, characteristic p 156
8.4 Normal subgroup growth 158
Notes 160
9 Soluble Groups 161
9.1 Metabelian groups 162
9.2 Residually nilpotent groups 164
9.3 Some finitely presented metabelian groups 167
9.4 Normal subgroup growth in metabelian groups 172
Notes 175
Contents xi
10 Proflnite Groups with Polynomial Subgroup Growth 177
10.1 Upper rank 180
10.2 Profinite groups with wPSG: structure 181
10.3 Quasi semisimple groups 187
10.4 Profinite groups with wPSG: characterization 194
10.5 Weak PSG = PSG 197
Notes 200
11 Probabilistic Methods 201
11.1 The probability measure 205
11.2 Generation probabilities 207
11.3 Maximal subgroups 209
11.4 Further applications 211
11.5 Pro p groups 214
Notes 217
12 Other Growth Conditions 219
12.1 Rank and bounded generation 225
12.2 Adelic groups 226
12.3 The structure of finite linear groups 229
12.4 Composition factors 230
12.5 BG, PIG and subgroup growth 233
12.6 Residually nilpotent groups 234
12.7 Arithmetic groups and the CSP 236
12.8 Examples 237
Notes 241
13 The Growth Spectrum 243
13.1 Products of alternating groups 244
13.2 Some finitely generated permutation groups 248
13.3 Some profinite groups with restricted composition factors . . 255
13.4 Automorphisms of rooted trees 260
Notes 266
14 Explicit Formulas and Asymptotics 269
14.1 Free groups and the modular group 269
14.2 Free products of finite groups 271
14.3 Modular subgroup arithmetic 274
14.4 Surface groups 277
Notes 283
15 Zeta Functions I: Nilpotent Groups 285
15.1 Local zeta functions as p adic integrals 290
15.2 Alternative methods 297
15.3 The zeta function of a nilpotent group 304
Notes 307
xii Contents
16 Zeta Functions II: p adic Analytic Groups 309
16.1 Integration on pro p groups 312
16.2 Counting subgroups in a p adic analytic group 313
16.3 Counting orbits 315
16.4 Counting p groups 316
Notes 318
Windows
1 Finite Group Theory 319
1 Hall subgroups and Sylow bases 319
2 Carter subgroups 320
3 The Fitting subgroup 320
4 The generalized Fitting subgroup 322
5 Tate s theorem 322
6 Rank and p rank 323
7 Schur multiplier 323
8 Powerful p groups 324
9 GL,, and Sym(n) 325
2 Finite Simple Groups 329
1 The list 330
2 Generators 331
3 Subgroups 332
4 Representations 332
5 Automorphisms 334
6 Schur multipliers 335
7 An elementary proof 335
3 Permutation Groups 337
1 Primitive groups 337
2 Groups with restricted sections 338
3 Subgroups of alternating groups 343
4 Profinite Groups 349
1 Completions 350
2 Free profinite groups 352
3 Profinite presentations 353
5 Pro p Groups 357
1 Generators and relations 357
2 Pro p groups of finite rank 359
3 Linear pro p groups over local fields 361
4 Automorphisms of finite p groups 363
5 Hall s enumeration principle 364
Contents xiii
6 Soluble Groups 367
1 Nilpotent groups 367
2 Soluble groups of finite rank 369
3 Finitely generated metabelian groups 372
7 Linear Groups 375
1 Soluble groups 375
2 Jordan s theorem 376
3 Monomial groups 376
4 Finitely generated groups 376
5 Lang s theorem 377
8 Linearity Conditions for Infinite Groups 379
1 Variations on Mal cev s local theorem 379
2 Groups that are residually of bounded rank 383
3 Applications of Ado s theorem 385
9 Strong Approximation for Linear Groups 389
1 A variant of the Strong Approximation Theorem 390
2 Subgroups of SLTl(Fp) 397
3 The Lubotzky alternative 400
4 Strong approximation in positive characteristic 406
10 Primes 409
1 The Prime Number Theorem 409
2 Arithmetic progressions and the
Bombieri Vinogradov theorem 411
3 Global fields and Chebotarev s theorem 413
11 Probability 415
12 p adic Integrals and Logic 419
1 Results 419
2 A peek inside the black box 421
Open Problems 425
1 Growth spectrum 425
2 Normal subgroup growth in pro p groups
and metabelian groups 428
3 The degree of f.g. nilpotent groups 428
4 Finite extensions 429
5 Soluble groups 429
6 Isospectral groups 429
7 Congruence subgroups, lattices in Lie groups 430
8 Other growth conditions 430
9 Zeta functions 431
Bibliography 433
Index 446
|
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| author | Lubotzky, Alexander Segal, Daniel 1947- |
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| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV017322978 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T11:17:47Z |
| institution | BVB |
| isbn | 3764369892 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010441681 |
| oclc_num | 51861897 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-20 DE-11 DE-384 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-20 DE-11 DE-384 DE-188 |
| physical | XXII, 453 S. 940 gr. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spellingShingle | Lubotzky, Alexander Segal, Daniel 1947- Subgroup growth Progress in mathematics Croissance de sous-groupes (Mathématiques) Groupes infinis Teoria dos grupos larpcal Álgebra larpcal Infinite groups Subgroup growth (Mathematics) Asymptotik (DE-588)4126634-1 gnd Untergruppe (DE-588)4224972-7 gnd Unendliche Gruppe (DE-588)4375539-2 gnd |
| subject_GND | (DE-588)4126634-1 (DE-588)4224972-7 (DE-588)4375539-2 |
| title | Subgroup growth |
| title_auth | Subgroup growth |
| title_exact_search | Subgroup growth |
| title_full | Subgroup growth Alexander Lubotzky ; Dan Segal |
| title_fullStr | Subgroup growth Alexander Lubotzky ; Dan Segal |
| title_full_unstemmed | Subgroup growth Alexander Lubotzky ; Dan Segal |
| title_short | Subgroup growth |
| title_sort | subgroup growth |
| topic | Croissance de sous-groupes (Mathématiques) Groupes infinis Teoria dos grupos larpcal Álgebra larpcal Infinite groups Subgroup growth (Mathematics) Asymptotik (DE-588)4126634-1 gnd Untergruppe (DE-588)4224972-7 gnd Unendliche Gruppe (DE-588)4375539-2 gnd |
| topic_facet | Croissance de sous-groupes (Mathématiques) Groupes infinis Teoria dos grupos Álgebra Infinite groups Subgroup growth (Mathematics) Asymptotik Untergruppe Unendliche Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010441681&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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