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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.Read more
- Only prerequisite is one semester of abstract algebra: accessible to undergraduate and beginning graduate students
- Over 150 exercises and 95 figures aid understanding and develop geometric intuition
- Modern approach with many contemporary results presented
Reviews & endorsements
"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 NewsSee more reviews
"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
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- Date Published: September 2008
- format: Paperback
- isbn: 9780521719773
- length: 244 pages
- dimensions: 228 x 152 x 13 mm
- weight: 0.36kg
- contains: 1 table 175 exercises
- availability: Available
Table of Contents
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
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