The theory of groups: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston
Allyn and Bacon
1973
|
| Edition: | 2. ed. |
| Series: | Allyn and Bacon series in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 342 S. |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Preface vii
1. Groups and Homomorphisms 1
2. The Isomorphism Theorems 11
Subgroups 11
Normal Subgroups and Quotient Groups 18
The Isomorphism Theorems 21
The Correspondence Theorem 24
3. Permutation Groups 27
Permutations 27
Cycles 28
Conjugates 34
The Simplicity of An 38
Some Representation Theorems 42
Counting Orbits 44
4. Finite Direct Products 49
Direct Products 49
The Basis Theorem 52
The Fundamental Theorem of Finite Abelian Groups 57
Modules and Matrices 60
The Remak Krull Schmidt Theorem 75
5. The Sylow Theorems 83
p Groups 83
The Sylow Theorems 85
Some Applications of the Sylow Theorems 89
6. Normal Series 96
Some Galois Theory 96
The Jordan Holder Theorem 103
Solvable Groups 108
A Theorem of P. Hall 112
Central Series and Nilpotent Groups 116
7. Extensions 127
The Extension Problem 127
Automorphism Groups 129
Semidirect Products 135
Factor Sets 141
The Schur Zassenhaus Lemma 148
v
VI CONTENTS
8. Some Simple Groups 152
Finite Fields 152
The General Linear Group 156
PSL(2, K) 160
PSL(m, K) 165
9. Infinite Abelian Groups 174
The First Reduction: Torsion and Torsion Free 174
The Second Reduction: Divisible and Reduced 179
Free Abelian Groups 187
Finitely Generated Abelian Groups 192
Torsion Groups 194
Torsion Free Groups 200
Grothendieck Groups 204
10. HOMOLOGICAL ALGEBRA 211
The Horn Functors 211
Definition of Ext 217
Pull Backs and Push Outs 219
The Ext Functors 228
11. Free Groups and Free Products 236
Generators and Relations 236
Edgepath Groups 243
Covering Complexes and the Nielsen Schreier Theorem 251
Free Products and the Kuros Theorem 262
Free Products with Amalgamated Subgroup 269
12. The Word Problem 277
Statement of the Problem 277
Turing Machines and Post s Theorem 279
Brit ton s Lemma 289
The Novikov Boone Theorem 298
An Imbedding Theorem of G. Higman 308
Appendices 322
I Some Major Algebraic Systems 322
II Equivalence Relations and Equivalence Classes 324
HI Functions 326
IV Zorn s Lemma 328
V Principal Ideal Domains 330
Bibliography 333
Notation 335
Index 337
|
| any_adam_object | 1 |
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| dewey-sort | 3512 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
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| publisher | Allyn and Bacon |
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| series2 | Allyn and Bacon series in advanced mathematics |
| spelling | Rotman, Joseph J. 1934- Verfasser (DE-588)120676826 aut The theory of groups an introduction Joseph J. Rotman 2. ed. Boston Allyn and Bacon 1973 IX, 342 S. txt rdacontent n rdamedia nc rdacarrier Allyn and Bacon series in advanced mathematics Groepentheorie gtt Group theory Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Gruppe Mathematik (DE-588)4022379-6 s DE-604 Gruppentheorie (DE-588)4072157-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012831828&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rotman, Joseph J. 1934- The theory of groups an introduction Groepentheorie gtt Group theory Gruppe Mathematik (DE-588)4022379-6 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4022379-6 (DE-588)4072157-7 (DE-588)4151278-9 |
| title | The theory of groups an introduction |
| title_auth | The theory of groups an introduction |
| title_exact_search | The theory of groups an introduction |
| title_full | The theory of groups an introduction Joseph J. Rotman |
| title_fullStr | The theory of groups an introduction Joseph J. Rotman |
| title_full_unstemmed | The theory of groups an introduction Joseph J. Rotman |
| title_short | The theory of groups |
| title_sort | the theory of groups an introduction |
| title_sub | an introduction |
| topic | Groepentheorie gtt Group theory Gruppe Mathematik (DE-588)4022379-6 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Groepentheorie Group theory Gruppe Mathematik Gruppentheorie Einführung |
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