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

ISBN-13: 9780521895453 / Angielski / Twarda / 2008 / 244 str.

John Meier

Opis

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.

Recenzje

'… an excellent introduction to geometric group theory. … Carefully chosen examples are an essential part of the exposition and they really help to understand general constructions.' EMS Newsletter

Spis treści

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.