Skew linear groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Publ.
1986
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society: London Mathematical Society lecture notes
118 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 253 S. |
| ISBN: | 0521339251 |
Staff View
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| 245 | 1 | 0 | |a Skew linear groups |c M. Shirvani and B. A. F. Wehrfritz |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
FOREWORD
1. BASIC CONCEPTS
1.1 Irreducibility 1
1.2 Absolute Irreducibility 10
1.3 Unipotence 17
1.4 Constructions 23
2. FINITE AND LOCALLY FINITE GROUPS
2.1 Finite Subgroups of Division Rings 44
2.2 The Schur Index 63
2.3 Locally Finite Skew Linear Groups of Positive Charcteristic 65
2.4 The Theorems of Zalesskii and Hartley fc Shahabi 67
2.5 Locally Finite Skew Linear Groups of Characteristic Zero 73
3. LOCALLY FINITE DIMENSIONAL DIVISION ALGEBRAS
3.1 General Techniques 80
3.2 Locally Nilpotent Groups 86
3.3 Locally Soluble Groups 95
3.4 The Upper Central Series 103
3.5 Engel Elements and Generalized Nilpotent Groups 114
4. DIVISION RINGS ASSOCIATED WITH POLYCYCLIC GROUPS
4.1 Generalities and Examples 123
4.2 Residual Finiteness 129
4.3 Residual Nilpotence 138
4.4 Division Rings of Quotients of Group Algebras 147
4.5 Free Subgroups of Normal Subgroups of General Linear Groups 154
4.6 Universal Enveloping Algebras of Lie Algebras 162
5. NORMAL SUBGROUPS OF ABSOLUTELY IRREDUCIBLE GROUPS
5.1 Normal Subgroups of Linear Groups 166
5.2 Autoaorphisma of Certain Semisimple Algebras 176
5.3 Recognizing Crossed Products 181
5.4 Locally Finite Normal Subgroups of Skew Linear Groups 192
5.5 Locally Finite Dimensional Division Algebras 199
5.6 Soluble Normal Subgroups of Skew Linear Groups 202
5.7 Generalized Soluble Groups 208
6 AN APPLICATION TO GROUP RINGS
6.1 Preliminaries 220
6.2 Soluble Groups 223
6.3 Locally Finite Groups 224
BIBLIOGRAPHY 227
NOTATION INDEX 237
AUTHOR INDEX 246
GENERAL INDEX 249
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| indexdate | 2024-07-09T15:16:05Z |
| institution | BVB |
| isbn | 0521339251 |
| language | English |
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| physical | 253 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Cambridge Univ. Publ. |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture notes |
| series2 | London Mathematical Society: London Mathematical Society lecture notes |
| spelling | Shirvani, M. Verfasser aut Skew linear groups M. Shirvani and B. A. F. Wehrfritz 1. publ. Cambridge u.a. Cambridge Univ. Publ. 1986 253 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture notes 118 Corps gauches Groupes finis Matrices, Groupes de Division rings Finite groups Matrix groups Schiefgruppenring (DE-588)4179550-7 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Schiefe lineare Gruppe gnd rswk-swf Schiefgruppenring (DE-588)4179550-7 s DE-604 Schiefe lineare Gruppe f Endliche Gruppe (DE-588)4014651-0 s Wehrfritz, Bertram A. F. Verfasser aut London Mathematical Society: London Mathematical Society lecture notes 118 (DE-604)BV000000130 118 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000361003&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shirvani, M. Wehrfritz, Bertram A. F. Skew linear groups London Mathematical Society: London Mathematical Society lecture notes Corps gauches Groupes finis Matrices, Groupes de Division rings Finite groups Matrix groups Schiefgruppenring (DE-588)4179550-7 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4179550-7 (DE-588)4014651-0 |
| title | Skew linear groups |
| title_auth | Skew linear groups |
| title_exact_search | Skew linear groups |
| title_full | Skew linear groups M. Shirvani and B. A. F. Wehrfritz |
| title_fullStr | Skew linear groups M. Shirvani and B. A. F. Wehrfritz |
| title_full_unstemmed | Skew linear groups M. Shirvani and B. A. F. Wehrfritz |
| title_short | Skew linear groups |
| title_sort | skew linear groups |
| topic | Corps gauches Groupes finis Matrices, Groupes de Division rings Finite groups Matrix groups Schiefgruppenring (DE-588)4179550-7 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Corps gauches Groupes finis Matrices, Groupes de Division rings Finite groups Matrix groups Schiefgruppenring Endliche Gruppe Schiefe lineare Gruppe |
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