Groups, Graphs and Trees: An Introduction to the Geometry of Infinite Groups

by John Meier

Overview

This outstanding new book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.

Product Details

ISBN-13:	9780521719773
Publisher:	Cambridge University Press
Publication date:	07/31/2008
Series:	London Mathematical Society Student Texts , #73
Edition description:	New Edition
Pages:	244
Product dimensions:	5.90(w) x 8.80(h) x 0.60(d)

About the Author

John Meier is a Professor in the Department of Mathematics at Lafayette College.

Table of Contents

Preface; 1. Cayley's theorems; 2. Groups generated by reflections; 3. Groups acting on trees; 4. Baumslag-Solitar groups; 5. Words and Dehn's word problem; 6. A finitely-generated, infinite, Torsion group; 7. Regular languages and normal forms; 8. The Lamplighter group; 9. The geometry of infinite groups; 10. Thompson's group; 11. The large-scale geometry of groups; Bibliography; Index.

Editorial Reviews

"Meier has the rare ability to make complex concepts accessible to novices while simultaneously challenging the experienced... With well-chosen illustrations and examples, Meier succeeds brilliantly in this unique approach."
Book News

"It is totally accessible to undergraduate students and would be a good textbook for an advanced undergraduate course in group theory, or a graduate course in geometric group theory."
Dmytro M. Savchuk, SUNY Binghamton for Mathematical Reviews

From the Publisher