The restricted Burnside problem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1993
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | London Mathematical Society: London Mathematical Society monographs / New series
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 256 S. |
| ISBN: | 0198537867 |
Internformat
MARC
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| 100 | 1 | |a Vaughan-Lee, Michael |d 19XX- |e Verfasser |0 (DE-588)1011425092 |4 aut | |
| 245 | 1 | 0 | |a The restricted Burnside problem |c Michael Vaughan-Lee |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Oxford |b Clarendon Press |c 1993 | |
| 300 | |a XIII, 256 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society: London Mathematical Society monographs / New series |v 8 | |
| 650 | 4 | |a Algèbre Lie | |
| 650 | 7 | |a Burnside, Problème de |2 ram | |
| 650 | 7 | |a Burnside, problèmes de |2 ram | |
| 650 | 4 | |a Exposant groupe | |
| 650 | 4 | |a Groupe localement fini | |
| 650 | 4 | |a Groupe nilpotent | |
| 650 | 7 | |a Groupes, Théorie des |2 ram | |
| 650 | 4 | |a Problème Burnside | |
| 650 | 4 | |a Sandwich | |
| 650 | 4 | |a Théorème Kostrikin | |
| 650 | 4 | |a Théorème Razmyslov | |
| 650 | 4 | |a Théorème Zelmanov | |
| 650 | 4 | |a Burnside problem | |
| 650 | 0 | 7 | |a Beschränkte Burnside-Vermutung |0 (DE-588)4246777-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Burnside-Vermutung |0 (DE-588)4147029-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804123260163457024 |
|---|---|
| adam_text | Contents
Notation xi
1. Basic concepts 1
1.1. Introduction 1
1.2. Lie rings and Lie algebras 3
1.3. Graded Lie algebras 11
1.4. Free Lie algebras 12
1.5. Varieties of groups and Lie algebras 20
1.6. Enveloping algebras 23
2. The associated Lie ring of a group 26
2.1. The lower central series 26
2.2. The lower exponent p central series 28
2.3. Associated Lie rings 31
2.4. Multilinear identities 33
2.5. A basis theorem 38
3. Kostrikin s Theorem 53
3.1. Kostrikin s Theorem for p = 2, 3, 5, and 7 53
3.2. Sandwich algebras 57
3.3. Kostrikin s Theorem for p 5 63
3.4. The locally nilpotent radical 65
4. Razmyslov s Theorem 67
4.1. Prime powers q = pk where p 3 and k 2 67
4.2. An auxiliary construction 69
4.3. A bilinear coupling 73
4.4. Some non solvable varieties of Lie rings 76
5. Groups of exponent two, three, and six 87
5.1. Exponent 2 87
5.2. Exponent 3 88
5.3. Exponent 6 90
6. Groups of exponent four 96
6.1. Local finiteness 96
6.2. Lie ring identities 97
6.3. Group commutator identities 107
6.4. Class and derived length 120
x Contents
6.5. Bounds on order 131
6.6. Further problems 141
6.7. Tables and lists of identities 142
7. Groups of prime exponent 146
7.1. Lie rings of groups of exponent p ^ 5 146
7.2. Exponent 5 148
7.3. Exponent 7 152
8. Groups of prime power exponent 154
8.1. Lie rings of groups of prime power exponent 154
8.2. Exponent 8 157
8.3. Exponent 9 160
9. Zelmanov s Theorem 161
9.1. A reduction theorem 162
9.2. (/ words 166
9.3. Odd characteristic 173
9.4. (/ polynomials 177
9.5. Characteristic 2 183
9.6. Jordan algebras 200
Appendix A 203
Appendix B 224
B.I. Coset enumeration 224
B.2. The nilpotent quotient algorithm for groups 227
B.3. Applications of the group nilpotent quotient algorithm 238
B.4. The nilpotent quotient algorithm for graded Lie rings 244
Bibliography 250
Author Index 253
Subject Index 255
|
| any_adam_object | 1 |
| author | Vaughan-Lee, Michael 19XX- |
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| ctrlnum | (OCoLC)27935616 (DE-599)BVBBV008931316 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV008931316 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:26:56Z |
| institution | BVB |
| isbn | 0198537867 |
| language | English |
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| owner_facet | DE-12 DE-824 DE-703 DE-11 |
| physical | XIII, 256 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Clarendon Press |
| record_format | marc |
| series2 | London Mathematical Society: London Mathematical Society monographs / New series |
| spelling | Vaughan-Lee, Michael 19XX- Verfasser (DE-588)1011425092 aut The restricted Burnside problem Michael Vaughan-Lee 2. ed. Oxford Clarendon Press 1993 XIII, 256 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society monographs / New series 8 Algèbre Lie Burnside, Problème de ram Burnside, problèmes de ram Exposant groupe Groupe localement fini Groupe nilpotent Groupes, Théorie des ram Problème Burnside Sandwich Théorème Kostrikin Théorème Razmyslov Théorème Zelmanov Burnside problem Beschränkte Burnside-Vermutung (DE-588)4246777-9 gnd rswk-swf Burnside-Vermutung (DE-588)4147029-1 gnd rswk-swf Beschränkte Burnside-Vermutung (DE-588)4246777-9 s DE-604 Burnside-Vermutung (DE-588)4147029-1 s 1\p DE-604 New series London Mathematical Society: London Mathematical Society monographs 8 (DE-604)BV045355493 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005889800&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Vaughan-Lee, Michael 19XX- The restricted Burnside problem Algèbre Lie Burnside, Problème de ram Burnside, problèmes de ram Exposant groupe Groupe localement fini Groupe nilpotent Groupes, Théorie des ram Problème Burnside Sandwich Théorème Kostrikin Théorème Razmyslov Théorème Zelmanov Burnside problem Beschränkte Burnside-Vermutung (DE-588)4246777-9 gnd Burnside-Vermutung (DE-588)4147029-1 gnd |
| subject_GND | (DE-588)4246777-9 (DE-588)4147029-1 |
| title | The restricted Burnside problem |
| title_auth | The restricted Burnside problem |
| title_exact_search | The restricted Burnside problem |
| title_full | The restricted Burnside problem Michael Vaughan-Lee |
| title_fullStr | The restricted Burnside problem Michael Vaughan-Lee |
| title_full_unstemmed | The restricted Burnside problem Michael Vaughan-Lee |
| title_short | The restricted Burnside problem |
| title_sort | the restricted burnside problem |
| topic | Algèbre Lie Burnside, Problème de ram Burnside, problèmes de ram Exposant groupe Groupe localement fini Groupe nilpotent Groupes, Théorie des ram Problème Burnside Sandwich Théorème Kostrikin Théorème Razmyslov Théorème Zelmanov Burnside problem Beschränkte Burnside-Vermutung (DE-588)4246777-9 gnd Burnside-Vermutung (DE-588)4147029-1 gnd |
| topic_facet | Algèbre Lie Burnside, Problème de Burnside, problèmes de Exposant groupe Groupe localement fini Groupe nilpotent Groupes, Théorie des Problème Burnside Sandwich Théorème Kostrikin Théorème Razmyslov Théorème Zelmanov Burnside problem Beschränkte Burnside-Vermutung Burnside-Vermutung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005889800&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045355493 |
| work_keys_str_mv | AT vaughanleemichael therestrictedburnsideproblem |