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

Name: Groups, Graphs and Trees An Introduction to the Geometry of Infinite Groups
Price: 42.75 USD
Availability: InStock
ISBN: 9780521719773

ISBN-10: 0521719771

ISBN-13: 9780521719773

Edition: 2008

Authors: John Meier

List price: $49.99

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Description:

Presenting 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…

Book details

List price: $49.99
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 7/31/2008
Binding: Paperback
Pages: 244
Size: 6.00" wide x 8.75" long x 0.50" tall
Weight: 0.792
Language: English



Preface



Cayley's Theorems



Cayley's Basic Theorem



Graphs



Symmetry Groups of Graphs



Orbits and Stabilizers



Generating Sets and Cayley Graphs



More Cayley Graphs



Symmetries of Cayley Graphs



Fundamental Domains and Generating Sets



Words and Paths



Groups Generated by Reflections



Groups Acting on Trees



Free Groups



F3 is a Subgroup of F2



Free Group Homomorphisms and Group Presentations



Free Groups and Actions on Trees



The Group Z3 * Z4



Free Products of Groups



Free Products of Finite Groups are Virtually Free



A Geometric View of Theorem 3.35



Finite Groups Acting on Trees



Serre's Property FA and Infinite Groups



Baumslag-Solitar Groups



Words and Dehn's Word Problem



Normal Forms



Dehn's Word Problem



The Word Problem and Cayley Graphs



The Cayley Graph of BS(1,2)



A Finitely Generated, Infinite Torsion Group



Regular Languages and Normal Forms



Regular Languages and Automata



Not All Languages are Regular



Regular Word Problem?



A Return to Normal Forms



Finitely Generated Subgroups of Free Groups



The Lamplighter Group



The Geometry of Infinite Groups



Gromov's Corollary, aka the Word Metric



The Growth of Groups, I



Growth and Regular Languages



Cannon Pairs



Cannon's Almost Convexity



Thompson's Group



The Large-Scale Geometry of Groups



Changing Generators



The Growth of Groups, II



The Growth of Thompson's Group



The Ends of Groups



The Freudenthal-Hopf Theorem



Two-Ended Groups



Commensurable Groups and Quasi-Isometry


Bibliography


Index