Book:Derek J.S. Robinson/A Course in the Theory of Groups/Second Edition

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Derek J.S. Robinson: A Course in the Theory of Groups (2nd Edition)

Published $1996$, Springer

ISBN 0-387-94461-3.


Subject Matter


Contents

Preface to the Second Edition
Preface to the First Edition
Notation
CHAPTER 1: Fundamental Concepts of Group Theory
1.1. Binary Operations, Semigroups, and Groups
1.2. Examples of Groups
1.3. Subgroups and Cosets
1.4. Homomorphisms and Quotient Groups
1.5. Endomorphisms and Automorphisms
1.6. Permutation Groups and Group Actions
CHAPTER 2: Free Groups and Presentations
2.1. Free Groups
2.2. Presentations of Groups
2.3. Varieties of Groups
CHAPTER 3: Decompositions of a Group
3.1. Series and Composition Series
3.2. Some Simple Groups
3.3. Direct Decompositions
CHAPTER 4: Abelian Groups
4.1. Torsion Groups and Divisible Groups
4.2. Direct Sums of Cyclic and Quasicyclic Groups
4.3. Pure Subgroups and p-Groups
4.4. Torsion-Free Groups
CHAPTER 5: Soluble and Nilpotent Groups
5.1. Abelian and Central Series
5.2. Nilpotent Groups
5.3. Groups of Prime-Power Order
5.4. Soluble Groups
CHAPTER 6: Free Groups and Free Products
6.1. Further Properties of Free Groups
6.2. Free Products of Groups
6.3. Subgroups of Free Products
6.4. Generalized Free Products
CHAPTER 7: Finite Permutation Groups
7.1. Multiple Transitivity
7.2. Primitive Permutation Groups
7.3. Classification of Sharply /c-Transitive Permutation Groups
7.4. The Mathieu Groups
CHAPTER 8: Representations of Groups
8.1. Representations and Modules
8.2. Structure of the Group Algebra
8.3. Characters
8.4. Tensor Products and Representations
8.5. Applications to Finite Groups
CHAPTER 9: Finite Soluble Groups
9.1. Hall π-Subgroups
9.2. Sylow Systems and System Normalizers
9.3. p-Soluble Groups
9.4. Supersoluble Groups
9.5. Formations
CHAPTER 10: The Transfer and Its Applications
10.1. The Transfer Homomorphism
10.2. Gain's Theorems
10.3. Frobenius's Criterion for p-Nilpotence
10.4. Thompson's Criterion for p-Nilpotence
10.5. Fixed-Point-Free Automorphisms
CHAPTER 11: The Theory of Group Extensions
11.1. Group Extensions and Covering Groups
11.2. Homology Groups and Cohomology Groups
11.3. The Gruenberg Resolution
11.4. Group-Theoretic Interpretations of the (Co)homology Groups
CHAPTER 12: Generalizations of Nilpotent and Soluble Groups
12.1. Locally Nilpotent Groups
12.2. Some Special Types of Locally Nilpotent Groups
12.3. Engel Elements and Engel Groups
12.4. Classes of Groups Defined by General Series
12.5. Locally Soluble Groups
CHAPTER 13: Subnormal Subgroups
13.1. Joins and Intersections of Subnormal Subgroups
13.2. Permutability and Subnormality
13.3. The Minimal Condition on Subnormal Subgroups
13.4. Groups in Which Normality Is a Transitive Relation
13.5. Automorphism Towers and Complete Groups
CHAPTER 14: Finiteness Properties
14.1. Finitely Generated Groups and Finitely Presented Groups
14.2. Torsion Groups and the Burnside Problems
14.3. Locally Finite Groups
14.4. 2-Groups with the Maximal or Minimal Condition
14.5. Finiteness Properties of Conjugates and Commutators
CHAPTER 15: Infinite Soluble Groups
15.1. Soluble Linear Groups
15.2. Soluble Groups with Finiteness Conditions on Abelian Subgroups
15.3. Finitely Generated Soluble Groups and the Maximal Condition on Normal Subgroups
15.4. Finitely Generated Soluble Groups and Residual Finiteness
15.5. Finitely Generated Soluble Groups and Their Frattini Subgroups
Bibliography
Index