P-automorphisms of finite p-groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1998
|
| Schriftenreihe: | London Mathematical Society: London Mathematical Society lecture note series
246 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 204 S. |
| ISBN: | 052159717X |
Internformat
MARC
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1998 | |
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Datensatz im Suchindex
| _version_ | 1804126536848113664 |
|---|---|
| adam_text | Contents
Preface viii
Introduction ix
Chapter 1. Preliminaries 1
§ 1.1. Groups 1
§ 1.2. Rings and modules 13
§ 1.3. Algebraic systems, varieties and free objects 17
Exercises 1 24
Chapter 2. Automorphisms and their fixed points 26
§ 2.1. Semidirect products 26
§ 2.2. Automorphisms as linear transformations 29
§ 2.3. Induced automorphisms of factor groups 32
Exercises 2 34
Chapter 3. Nilpotent and soluble groups 36
§ 3.1. The lower central series 36
§ 3.2. Nilpotent groups 38
§ 3.3. Soluble groups and varieties 42
§ 3.4. Nilpotency criteria for soluble groups 46
Exercises 3 48
Chapter 4. Finite p groups 51
§4.1. Basic properties 51
§4.2. A theorem of P.Hall 54
Exercises 4 56
Chapter 5. Lie rings 57
§ 5.1. Definitions and basic properties 57
§ 5.2. Nilpotent and soluble Lie rings 62
§ 5.3. Free Lie rings 66
Exercises 5 71
vi Contents
Chapter 6. Associated Lie rings 74
§ 6.1. Definition 74
§ 6.2. Basic properties 77
§ 6.3. Some applications 79
Exercises 6 81
Chapter 7. Regular automorphisms of Lie rings 83
§ 7.1. Graded Lie rings 83
§ 7.2. Combinatorial consequences 88
§ 7.3. Regular automorphisms 90
Exercises 7 93
Chapter 8. Almost regular automorphism of order p:
almost nilpotency of p bounded class 95
Exercises 8 99
Chapter 9. The Baker—Hausdorff Formula
and nilpotent Q powered groups 101
§ 9.1. Free nilpotent groups 101
§ 9.2. The Baker Hausdorff Formula 104
§ 9.3. Nilpotent Q powered groups 109
Exercises 9 112
Chapter 10. The correspondences of A. I. Mal cev
and M. Lazard 113
§ 10.1. The Mal cev Correspondence 113
§ 10.2. The Lazard Correspondence 121
Exercises 10 128
Chapter 11. Powerful p groups 130
§ 11.1. Definitions and basic properties 130
§ 11.2. Finite p groups of bounded rank 135
Exercises 11 138
Chapter 12. Almost regular automorphism of order pn:
almost solubility of p™ bounded derived length .. 140
§ 12.1. Uniformly powerful case 140
§ 12.2. Application of the Mal cev Correspondence 143
§ 12.3. Almost solubility of ^ bounded derived length 146
Exercises 12 150
Contents vii
Chapter 13. p Automorphisms with p fixed points 151
§ 13.1. Abelian p groups 152
§ 13.2. Reduction to Lie rings 155
§ 13.3. The Lie ring theorem 160
Exercises 13 165
Chapter 14. Automorphism of order p with pm fixed points:
almost nilpotency of m bounded class 166
§ 14.1. Almost solubility of m bounded derived length 167
§ 14.2. Almost nilpotency of m bounded class 180
Exercises 14 189
Bibliography 190
Index of names 198
Subject Index 199
List of symbols 203
|
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| building | Verbundindex |
| bvnumber | BV011949186 |
| classification_rvk | SI 320 |
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| discipline | Mathematik |
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| id | DE-604.BV011949186 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:19:01Z |
| institution | BVB |
| isbn | 052159717X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008078725 |
| oclc_num | 605316550 |
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| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XVII, 204 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spelling | Chuchro, Evgenij I. Verfasser aut P-automorphisms of finite p-groups E. I. Khukhro Cambridge [u.a.] Cambridge Univ. Press 1998 XVII, 204 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture note series 246 Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Automorphismus (DE-588)4143709-3 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Automorphismus (DE-588)4143709-3 s DE-604 London Mathematical Society: London Mathematical Society lecture note series 246 (DE-604)BV000000130 246 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008078725&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chuchro, Evgenij I. P-automorphisms of finite p-groups London Mathematical Society: London Mathematical Society lecture note series Endliche Gruppe (DE-588)4014651-0 gnd Automorphismus (DE-588)4143709-3 gnd |
| subject_GND | (DE-588)4014651-0 (DE-588)4143709-3 |
| title | P-automorphisms of finite p-groups |
| title_auth | P-automorphisms of finite p-groups |
| title_exact_search | P-automorphisms of finite p-groups |
| title_full | P-automorphisms of finite p-groups E. I. Khukhro |
| title_fullStr | P-automorphisms of finite p-groups E. I. Khukhro |
| title_full_unstemmed | P-automorphisms of finite p-groups E. I. Khukhro |
| title_short | P-automorphisms of finite p-groups |
| title_sort | p automorphisms of finite p groups |
| topic | Endliche Gruppe (DE-588)4014651-0 gnd Automorphismus (DE-588)4143709-3 gnd |
| topic_facet | Endliche Gruppe Automorphismus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008078725&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT chuchroevgeniji pautomorphismsoffinitepgroups |