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

London Mathematical Society Student Texts

by John Meier

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.

Genres: Mathematics

244 pages, Paperback

First published July 31, 2008

Reviews

[Chris · Rating 4 out of 5]

More people should be aware of geometric group theory, but the existing sources are advanced. This is a gentler one.

If you know a computer programmer who talks way too much about trees, B-trees, graphs, greplin, and so on, buy this for them---a delicious slice of humble pie.

[Siddharth · Rating 4 out of 5]

Nice exposition of baas-serre theory, the lamplighter group, growth of groups, and gromov's study of hyperbolic groups.

[Jhoste · Rating 5 out of 5]

Excellent well written book at graduate math level.