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OverviewPresenting groups in a formal, abstract algebraic manner is both useful and powerful, yet it avoids a fascinating geometric perspective on group theory - which is also useful and powerful, particularly in the study of infinite groups. This 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. Full Product DetailsAuthor: John Meier (Lafayette College, Pennsylvania)Publisher: Cambridge University Press Imprint: Cambridge University Press (Virtual Publishing) Volume: 73 ISBN: 9781139167505ISBN 10: 1139167502 Publication Date: 05 June 2012 Audience: Professional and scholarly , Professional & Vocational Format: Undefined Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsPreface; 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.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.' SciTech Book News '... 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.' Mathematical Review '... 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 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 '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.' SciTech Book News '... 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.' Mathematical Review '... 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 Author InformationJohn Meier is a Professor in the Department of Mathematics at Lafayette College. Tab Content 6Author Website:Countries AvailableAll regions |
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