Introduction to Group Theory

This book quickly introduces beginners to general group theory and then focuses on three main themes: finite group theory, including sporadic groups; combinatorial and geometric group theory, including the Bass - Serre theory of groups acting on trees; the theory of train tracks by Bestvina and Handel for automorphisms of free groups.

With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful theory of train tracks is illustrated by two nontrivial examples.

Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists.

Reviews

The text should be welcomed by those who want exposure to the application of group theory within a nonstandard geometric environment.

Zentralblatt MATH

Contents

1 Introduction to finite group theory
2 Introduction to combinatorial group theory
3 Automorphisms of free groups and train tracks
Appendix. The Perron-Frobenius Theorem
Solutions to selected exercises
Bibliography
Index