HOME > Detail View

Detail View

A course in the theory of groups 2nd ed

A course in the theory of groups 2nd ed (Loan 10 times)

Material type
단행본
Personal Author
Robinson, Derek John Scott.
Title Statement
A course in the theory of groups / Derek J. S. Robinson.
판사항
2nd ed.
Publication, Distribution, etc
New York :   Springer-Verlag,   1995.  
Physical Medium
xvii, 499 p. : Ill. ; 24 cm.
Series Statement
Graduate texts in mathematics ;80
ISBN
0387944613 (hardcover : acid-free)
Bibliography, Etc. Note
Includes bibliographical references (p. 491-499) and index.
Subject Added Entry-Topical Term
Group theory.
000 00817camuuu2002778a 4500
001 000000425749
003 OCoLC
005 19961119111217.0
008 950125s1995 nyua b 001 0 eng
010 ▼a 95004025
020 ▼a 0387944613 (hardcover : acid-free)
040 ▼a DLC ▼c DLC
049 1 ▼l 111068150
050 0 0 ▼a QA174.2 ▼b .R63 1995
082 0 0 ▼a 512/.2 ▼2 20
090 ▼a 512.2 ▼b R659c2
100 1 ▼a Robinson, Derek John Scott.
245 1 2 ▼a A course in the theory of groups / ▼c Derek J. S. Robinson.
250 ▼a 2nd ed.
260 ▼a New York : ▼b Springer-Verlag, ▼c 1995.
263 ▼a 9507
300 ▼a xvii, 499 p. : ▼b Ill. ; ▼c 24 cm.
440 0 ▼a Graduate texts in mathematics ; ▼v 80
504 ▼a Includes bibliographical references (p. 491-499) and index.
650 0 ▼a Group theory.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/Western Books/ Call Number 512.2 R659c2 Accession No. 111068150 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents


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
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 k ­ 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 π ­ 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
CHAPTER 10
 The Transfer and Its Applications = 285
  10. 1. The Transfer Homomorphism = 285
  10. 2. Gr$${\ddot u}$$n'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
  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


New Arrivals Books in Related Fields