Topics in group theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Springer
2000
|
| Series: | Springer undergraduate mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 255 S. graph. Darst. |
| ISBN: | 1852332352 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface vii
Contents xi
List of Figures xv
The Greek Alphabet xvi
1. The Elements 1
1.1 Basic Results 1
1.2 Where Do Groups Come From? 14
1.3 Cosets 19
1.4 Subgroup Generation 29
1.5 Finite Generation 31
2. Structure 43
2.1 Conjugacy 46
2.2 Normal Subgroups 48
2.3 Factor Groups 49
2.4 Kernels and Images 53
2.5 Isomorphisms 59
2.6 Internal Direct Products 71
2.7 Finite Abelian Groups 74
2.8 Finitely Generated Abelian Groups 79
2.9 Semi direct Products 84
2.10 Wreath Products 86
3. Action 89
3.1 Permutation Groups 89
3.2 Conjugacy in the Symmetric Group 98
3.3 Group Actions 103
3.4 Orbits Form Partitions 105
3.5 Conjugacy Revisited 110
3.6 Enumeration 110
3.7 Group Theoretic Consequences 113
3.8 Finite p groups 116
3.9 Multiple Transitivity and Primitivity 120
4. Entertainments 125
4.1 The Finite Case 126
4.2 Infinite Groups 148
4.2.1 Infinite Simple Groups 148
4.2.2 An Infinite Alternating Group 149
4.2.3 The Transfer Map 154
4.3 The Derived Group 155
5. Law 159
5.1 The Commutator Calculus 159
5.2 The Derived Group Revisited 161
5.3 Nilpotent Groups 168
5.4 Varieties of Groups 171
5.5 Upper and Lower Central Series 178
5.6 Soluble Groups 184
6. Presentations 189
6.1 Informalities 189
6.2 The Rational Numbers 193
6.2.1 The Rationals Mark I 193
6.2.2 The Rationals Mark II 194
6.3 Tigers 195
6.3.1 Free Groups 200
6.4 Presentations and Free Groups 203
6.4.1 Standard Sloppy Notation 204
6.4.2 Commutator Subgroups 204
6.4.3 Tietze Transformations 205
6.5 Decideability Problems 206
6.6 The Knuth Bendix Procedure 208
6.7 Church Rosser and Confluence 210
6.8 Normal Forms 213
6.9 Knuth Bendix for Strings 213
7. Appendix A: Fields 219
7.1 The Axioms 219
7.2 Finite Fields 221
8. Appendix B: Relations and Orderings 229
8.1 Orderings 231
8.2 Chain Conditions 234
8.3 Zorn s Lemma 237
Further Reading 239
Solutions 241
Index 253
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:38:46Z |
| institution | BVB |
| isbn | 1852332352 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008912502 |
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| physical | XIII, 255 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate mathematics series |
| spelling | Smith, Geoff Verfasser aut Topics in group theory Geoff Smith and Olga Tabachnikova London [u.a.] Springer 2000 XIII, 255 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer undergraduate mathematics series Groupes, Théorie des Teoria dos grupos larpcal Álgebra larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Tabachnikova, Olga 1967- Verfasser (DE-588)121866343 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008912502&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smith, Geoff Tabachnikova, Olga 1967- Topics in group theory Groupes, Théorie des Teoria dos grupos larpcal Álgebra larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 |
| title | Topics in group theory |
| title_auth | Topics in group theory |
| title_exact_search | Topics in group theory |
| title_full | Topics in group theory Geoff Smith and Olga Tabachnikova |
| title_fullStr | Topics in group theory Geoff Smith and Olga Tabachnikova |
| title_full_unstemmed | Topics in group theory Geoff Smith and Olga Tabachnikova |
| title_short | Topics in group theory |
| title_sort | topics in group theory |
| topic | Groupes, Théorie des Teoria dos grupos larpcal Álgebra larpcal Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Groupes, Théorie des Teoria dos grupos Álgebra Group theory Gruppentheorie |
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