In preparing this new edition I have tried to keep the changes to a minimum, on the principle that one should not meddle with a relatively successful text.Thus the general form of the book remains the same.Naturally I have taken the opportunity to correct the errors of which I was aware.Also the text has been updated at various points, some proofs have been improved, and lastly about thirty additional exercises are included.

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 Abielian Groups

CHAPTER 5 Soluble and Nilpotent Groups

CHAPTER 6 Free Groups and Free Products

CHAPTER 7 Finite Permuation Groups

CHAPTER 8 Representations of Groups

CHAPTER 9 Finite Soluble Groups

CHAPTER 10 The Transfer and Its Applications

CHAPTER 11 The Theory of Group Eltensions

CHAPTER 12 Generalization of Nilpotent and Soluble Groups

CHAPTER 13 Subnormal Subgroups

CHAPTER 14 Finiteness Properties

CHAPTER 15 Infinite Souluble Groups

Bibliography

Index