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Introduction to Group Theory
EMS Textbooks in Mathematics

Oleg Bogopolski (TU Dortmund, Germany)

Introduction to Group Theory

ISBN print 978-3-03719-041-8, ISBN online 978-3-03719-541-3
DOI 10.4171/041
February 2008, 187 pages, hardcover, 16.5 x 23.5 cm.
38.00 Euro

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.

Keywords: Simple groups, sporadic groups, Steiner systems, codes, free products with amalgamation, HNN extensions, actions on trees, free groups and their automorphisms, train tracks

Further Information

Review in Zentralblatt MATH 05246364

Review in MR 2396717 (2009c:20001)

MAA Reviews

EMS Review