An introduction to the theory of groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1995
|
| Ausgabe: | 4. ed. |
| Schriftenreihe: | Graduate texts in mathematics
148 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 513 S. graph. Darst. |
| ISBN: | 3540942858 0387942858 9781461286868 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to the theory of groups |c Joseph J. Rotman |
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| 264 | 1 | |a New York u.a. |b Springer |c 1995 | |
| 300 | |a XIV, 513 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 148 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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Datensatz im Suchindex
| _version_ | 1804124129885945856 |
|---|---|
| adam_text | Contents
Preface to the Fourth Edition vii
From Preface to the Third Edition ix
To the Reader xv
Chapter 1
Groups and Homomorphisms 1
Permutations 2
Cycles 3
Factorization into Disjoint Cycles 6
Even and Odd Permutations 7
Semigroups 10
Groups 12
Homomorphisms 16
Chapter 2
The Isomorphism Theorems 20
Subgroups 20
Lagrange s Theorem 24
Cyclic Groups 28
Normal Subgroups 29
Quotient Groups 32
The Isomorphism Theorems 35
Correspondence Theorem 37
Direct Products 40
xii Contents
Chapter 3
Symmetric Groups and G Sets 43
Conjugates 43
Symmetric Groups 46
The Simplicity of An 50
Some Representation Theorems 51
G Sets 55
Counting Orbits 58
Some Geometry 63
Chapter 4
The Sylow Theorems 73
p Groups 73
The Sylow Theorems 78
Groups of Small Order 82
Chapter 5
Normal Series 89
Some Galois Theory 91
The Jordan Holder Theorem 98
Solvable Groups 102
Two Theorems of P. Hall 108
Central Series and Nilpotent Groups 112
p Groups 119
Chapter 6
Finite Direct Products 125
The Basis Theorem 125
The Fundamental Theorem of Finite Abelian Groups 131
Canonical Forms; Existence 133
Canonical Forms; Uniqueness 141
The Krull Schmidt Theorem 144
Operator Groups 151
Chapter 7
Extensions and Cohomology 154
The Extension Problem 154
Automorphism Groups 156
Semidirect Products 167
Wreath Products 172
Factor Sets 178
Theorems of Schur Zassenhaus and Gaschiitz 188
Transfer and Burnside s Theorem 193
Projective Representations and the Schur Multiplier 201
Derivations 211
Contents xiii
Chapter 8
Some Simple Linear Groups 217
Finite Fields 217
The General Linear Group 219
PSL(2, K) 224
PSL(m, K) 227
Classical Groups 234
Chapter 9
Permutations and the Mathieu Groups 247
Multiple Transitivity 247
Primitive G Sets 256
Simplicity Criteria 259
Affine Geometry 264
Projective Geometry 272
Sharply 3 Transitive Groups 281
Mathieu Groups 286
Steiner Systems 293
Chapter 10
Abelian Groups 307
Basics 307
Free Abelian Groups 312
Finitely Generated Abelian Groups 318
Divisible and Reduced Groups 320
Torsion Groups 325
Subgroups of Q 331
Character Groups 335
Chapter 11
Free Groups and Free Products 343
Generators and Relations 343
Semigroup Interlude 349
Coset Enumeration 351
Presentations and the Schur Multiplier 358
Fundamental Groups of Complexes 366
Tietze s Theorem 374
Covering Complexes 377
The Nielsen Schreier Theorem 383
Free Products 388
The Kurosh Theorem 391
The van Kampen Theorem 394
Amalgams 401
HNN Extensions 407
xiv Contents
Chapter 12
The Word Problem 418
Introduction 418
Turing Machines 420
The Markov Post Theorem 425
The Novikov Boone Britton Theorem: Sufficiency of Boone s
Lemma 430
Cancellation Diagrams 433
The Novikov Boone Britton Theorem: Necessity of Boone s
Lemma 438
The Higman Imbedding Theorem 450
Some Applications 464
Epilogue 471
Appendix I
Some Major Algebraic Systems 475
Appendix II
Equivalence Relations and Equivalence Classes 477
Appendix III
Functions 479
Appendix IV
Zorn s Lemma 481
Appendix V
Countability 483
Appendix VI
Commutative Rings 485
Bibliography 495
Notation 498
Index 503
|
| any_adam_object | 1 |
| author | Rotman, Joseph J. 1934- |
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| author_variant | j j r jj jjr |
| building | Verbundindex |
| bvnumber | BV009780048 |
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| classification_tum | MAT 200f |
| ctrlnum | (OCoLC)246649468 (DE-599)BVBBV009780048 |
| 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 | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV009780048 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:40:46Z |
| institution | BVB |
| isbn | 3540942858 0387942858 9781461286868 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006471647 |
| oclc_num | 246649468 |
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| physical | XIV, 513 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Rotman, Joseph J. 1934- Verfasser (DE-588)120676826 aut An introduction to the theory of groups Joseph J. Rotman 4. ed. New York u.a. Springer 1995 XIV, 513 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 148 Hier auch später erschienene, unveränderte Nachdrucke Gruppentheorie Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 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 Graduate texts in mathematics 148 (DE-604)BV000000067 148 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006471647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rotman, Joseph J. 1934- An introduction to the theory of groups Graduate texts in mathematics Gruppentheorie Gruppentheorie (DE-588)4072157-7 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4022379-6 (DE-588)4151278-9 |
| title | An introduction to the theory of groups |
| title_auth | An introduction to the theory of groups |
| title_exact_search | An introduction to the theory of groups |
| title_full | An introduction to the theory of groups Joseph J. Rotman |
| title_fullStr | An introduction to the theory of groups Joseph J. Rotman |
| title_full_unstemmed | An introduction to the theory of groups Joseph J. Rotman |
| title_short | An introduction to the theory of groups |
| title_sort | an introduction to the theory of groups |
| topic | Gruppentheorie Gruppentheorie (DE-588)4072157-7 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| topic_facet | Gruppentheorie Gruppe Mathematik Einführung |
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