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

Subject Matter

 * Group Theory

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