Groups, Graphs and Trees An Introduction to the Geometry of Infinite Groups [Paperback]

This book presents an accessible and engaging approach to geometric group theory; ideal for advanced undergraduates.This book presents a modern, geometric approach to group theory. An accessible and engaging approach to the subject, with many exercises and figures to develop geometric intuition. Ideal for advanced undergraduates, it will also interest graduate students and researchers as a gentle introduction to geometric group theory.This book presents a modern, geometric approach to group theory. An accessible and engaging approach to the subject, with many exercises and figures to develop geometric intuition. Ideal for advanced undergraduates, it will also interest graduate students and researchers as a gentle introduction to geometric group theory.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.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. Meierl“%