A course in the theory of groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY u.a.
Springer
1996
|
| Edition: | 2. ed. |
| Series: | Graduate texts in mathematics
80 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 499 S. graph. Darst. |
| ISBN: | 0387944613 |
Staff View
MARC
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| 245 | 1 | 0 | |a A course in the theory of groups |c Derek J. S. Robinson |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York, NY u.a. |b Springer |c 1996 | |
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 80 | |
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition vii
Preface to the First Edition viii
Notation xv
CHAPTER 1
Fundamental Concepts of Group Theory 1
1.1. Binary Operations, Semigroups, and Groups 1
1.2. Examples of Groups 4
1.3. Subgroups and Cosets 8
1.4. Homomorphisms and Quotient Groups 17
1.5. Endomorphisms and Automorphisms 25
1.6. Permutation Groups and Group Actions 31
CHAPTER 2
Free Groups and Presentations 44
2.1. Free Groups 44
2.2. Presentations of Groups 50
2.3. Varieties of Groups 56
CHAPTER 3
Decompositions of a Group 63
3.1. Series and Composition Series 63
3.2. Some Simple Groups 71
3.3. Direct Decompositions 80
xi
xii Contents
CHAPTER 4
Abelian Groups 93
4.1. Torsion Groups and Divisible Groups 93
4.2. Direct Sums of Cyclic and Quasicyclic Groups 98
4.3. Pure Subgroups and p Groups 106
4.4. Torsion Free Groups 114
CHAPTER 5
Soluble and Nilpotent Groups 121
5.1. Abelian and Central Series 121
5.2. Nilpotent Groups 129
5.3. Groups of Prime Power Order 139
5.4. Soluble Groups 147
CHAPTER 6
Free Groups and Free Products 159
6.1. Further Properties of Free Groups 159
6.2. Free Products of Groups 167
6.3. Subgroups of Free Products 174
6.4. Generalized Free Products 184
CHAPTER 7
Finite Permutation Groups 192
7.1. Multiple Transitivity 192
7.2. Primitive Permutation Groups 197
7.3. Classification of Sharply fc Transitive Permutation Groups 203
7.4. The Mathieu Groups 208
CHAPTER 8
Representations of Groups 213
8.1. Representations and Modules 213
8.2. Structure of the Group Algebra 223
8.3. Characters 226
8.4. Tensor Products and Representations 235
8.5. Applications to Finite Groups 246
CHAPTER 9
Finite Soluble Groups 252
9.1. Hall re Subgroups 252
9.2. Sylow Systems and System Normalizers 261
9.3. p Soluble Groups 269
9.4. Supersoluble Groups 274
9.5. Formations 277
Contents xiii
CHAPTER 10
The Transfer and Its Applications 285
10.1. The Transfer Homomorphism 285
10.2. Griin s Theorems 292
10.3. Frobenius s Criterion for p Nilpotence 295
10.4. Thompson s Criterion for p Nilpotence 298
10.5. Fixed Point Free Automorphisms 305
CHAPTER 11
The Theory of Group Extensions 310
11.1. Group Extensions and Covering Groups 310
11.2. Homology Groups and Cohomology Groups 326
11.3. The Gruenberg Resolution 333
11.4. Group Theoretic Interpretations of the (Co)homology Groups 341
CHAPTER 12
Generalizations of Nilpotent and Soluble Groups 356
12.1. Locally Nilpotent Groups 356
12.2. Some Special Types of Locally Nilpotent Groups 363
12.3. Engel Elements and Engel Groups 369
12.4. Classes of Groups Defined by General Series 376
12.5. Locally Soluble Groups 381
CHAPTER 13
Subnormal Subgroups 385
13.1. Joins and Intersections of Subnormal Subgroups 385
13.2. Permutability and Subnormality 393
13.3. The Minimal Condition on Subnormal Subgroups 396
13.4. Groups in Which Normality Is a Transitive Relation 402
13.5. Automorphism Towers and Complete Groups 408
CHAPTER 14
Finiteness Properties 416
14.1. Finitely Generated Groups and Finitely Presented Groups 416
14.2. Torsion Groups and the Burnside Problems 422
14.3. Locally Finite Groups 429
14.4. 2 Groups with the Maximal or Minimal Condition 437
14.5. Finiteness Properties of Conjugates and Commutators 439
CHAPTER 15
Infinite Soluble Groups 450
15.1. Soluble Linear Groups 450
15.2. Soluble Groups with Finiteness Conditions on Abelian Subgroups 455
xiv Contents
15.3. Finitely Generated Soluble Groups and the Maximal Condition
on Normal Subgroups 461
15.4. Finitely Generated Soluble Groups and Residual Finiteness 470
15.5. Finitely Generated Soluble Groups and Their Frattini Subgroups 474
Bibliography 479
Index 491
|
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| indexdate | 2024-07-09T17:54:42Z |
| institution | BVB |
| isbn | 0387944613 |
| language | English |
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| publishDate | 1996 |
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| spelling | Robinson, Derek John Scott 1938- Verfasser (DE-588)1017969213 aut A course in the theory of groups Derek J. S. Robinson 2. ed. New York, NY u.a. Springer 1996 XVII, 499 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 80 Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s DE-604 Graduate texts in mathematics 80 (DE-604)BV000000067 80 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007024764&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Robinson, Derek John Scott 1938- A course in the theory of groups Graduate texts in mathematics Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 |
| title | A course in the theory of groups |
| title_auth | A course in the theory of groups |
| title_exact_search | A course in the theory of groups |
| title_full | A course in the theory of groups Derek J. S. Robinson |
| title_fullStr | A course in the theory of groups Derek J. S. Robinson |
| title_full_unstemmed | A course in the theory of groups Derek J. S. Robinson |
| title_short | A course in the theory of groups |
| title_sort | a course in the theory of groups |
| topic | Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Group theory Gruppentheorie |
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