Book Details

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

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Further Information

Review in Zentralblatt MATH 05246364

Review in MR 2396717 (2009c:20001)

MAA Reviews

EMS Review

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