Introduction to Group Theory
Oleg BogopolskiTU Dortmund, Germany
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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.