Unit groups of group rings:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman Scientific & Technical
1989
|
| Edition: | 1. publ. |
| Series: | Pitman monographs and surveys in pure and applied mathematics
47 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 393 S. |
| ISBN: | 0470213698 0582023416 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction vii
Notation xi
1 Preliminaries 1
1. Notation and terminology 1
2. Assumed results 3
2 Group rings 9
1. Definitions and elementary properties 9
2. Some module isomorphisms 20
3. Trace of idempotents 25
3 General properties of U(RG) 40
1. Elementary results 41
2. Units of finite order 49
3. Trivial units 59
4. Unique product groups 67
5. The isomorphism problem 78
6. Finite subgroups of V(ZG) 89
7. Solvability and nilpotence of U(ZG) 92
8. Solvability of U(FG), Fa field 100
9. Units of ZSj 108
4 Unit groups of commutative group rings 114
1. Direct decompositions 115
2. Splitting groups 121
3. Conditions for RG to be indecomposable or reduced 127
4. Finite generation of U(RG) 136
5. May s theorem 150
6. Integral domains of characteristic 0 159
7. Indecomposable rings 164
vi CONTENTS
8. Direct factor theorems 171
A. Preliminary results 172
B. Direct factor property 175
C. Direct factor problem for fields of characteristic p 0 178
D. Direct factor problem for /^ groups 184
9. Splitting group algebras 193
A. Preliminary results 194
B. A nonsplitting group G with splitting FG for any field F 197
C. Algebraic number fields 200
10. The Ulm Kaplansky invariants of V(FG) 207
11. The torsion free rank of V(FG) 215
12. The isomorphism problem 220
A. Indecomposable rings of characteristic 0 221
B. Fields of characteristic p 0 227
C. Ullery s conjecture 231
D. Algebraically closed fields 236
E. Finite groups 240
F. Countable p groups 247
G. Real group algebras 250
13. The isomorphism class of U(ZG) 256
14. Bass independence theorem 261
15. Effective construction of units of ZG 266
16. The unitary subgroup of U(ZG) 274
5 Conjugacy of finite subgroups of V(ZPG) 283
1. Preliminaries 283
2. A general result and its applications 287
3. Relative traces, permutation modules and related results 292
4. Proof of Theorem 2.1 304
6 Units of metabelian integral group rings 317
1. Torsion free complements 317
A. Preliminary results 318
B. Main results 326
2. A description of U(ZG), G dihedral of order 2p 337
3. A conjecture of Zassenhaus 349
A. Preliminary results 350
B. Certain types of metabelian groups 359
C. Metabelian groups with faithful and irreducible actions 366
Bibliography 375
Index 391
|
| any_adam_object | 1 |
| author | Karpilovsky, Gregory 1940- |
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| bvnumber | BV003431356 |
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| classification_tum | MAT 200f |
| ctrlnum | (OCoLC)18628957 (DE-599)BVBBV003431356 |
| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV003431356 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:59:50Z |
| institution | BVB |
| isbn | 0470213698 0582023416 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002171597 |
| oclc_num | 18628957 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-703 DE-739 DE-29T DE-634 DE-11 |
| physical | XIII, 393 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Longman Scientific & Technical |
| record_format | marc |
| series | Pitman monographs and surveys in pure and applied mathematics |
| series2 | Pitman monographs and surveys in pure and applied mathematics |
| spelling | Karpilovsky, Gregory 1940- Verfasser (DE-588)131816357 aut Unit groups of group rings Gregory Karpilovsky 1. publ. Harlow, Essex Longman Scientific & Technical 1989 XIII, 393 S. txt rdacontent n rdamedia nc rdacarrier Pitman monographs and surveys in pure and applied mathematics 47 Commutative rings Group rings Unit groups (Ring theory) Kommutativer Ring (DE-588)4164825-0 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Einfache Gruppe (DE-588)4123107-7 gnd rswk-swf Gruppenring (DE-588)4158469-7 gnd rswk-swf Einfache Gruppe (DE-588)4123107-7 s Gruppenring (DE-588)4158469-7 s DE-604 Gruppentheorie (DE-588)4072157-7 s Kommutativer Ring (DE-588)4164825-0 s Pitman monographs and surveys in pure and applied mathematics 47 (DE-604)BV000022446 47 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002171597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Karpilovsky, Gregory 1940- Unit groups of group rings Pitman monographs and surveys in pure and applied mathematics Commutative rings Group rings Unit groups (Ring theory) Kommutativer Ring (DE-588)4164825-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Einfache Gruppe (DE-588)4123107-7 gnd Gruppenring (DE-588)4158469-7 gnd |
| subject_GND | (DE-588)4164825-0 (DE-588)4072157-7 (DE-588)4123107-7 (DE-588)4158469-7 |
| title | Unit groups of group rings |
| title_auth | Unit groups of group rings |
| title_exact_search | Unit groups of group rings |
| title_full | Unit groups of group rings Gregory Karpilovsky |
| title_fullStr | Unit groups of group rings Gregory Karpilovsky |
| title_full_unstemmed | Unit groups of group rings Gregory Karpilovsky |
| title_short | Unit groups of group rings |
| title_sort | unit groups of group rings |
| topic | Commutative rings Group rings Unit groups (Ring theory) Kommutativer Ring (DE-588)4164825-0 gnd Gruppentheorie (DE-588)4072157-7 gnd Einfache Gruppe (DE-588)4123107-7 gnd Gruppenring (DE-588)4158469-7 gnd |
| topic_facet | Commutative rings Group rings Unit groups (Ring theory) Kommutativer Ring Gruppentheorie Einfache Gruppe Gruppenring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002171597&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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