How groups grow
 Author/Creator
 Mann, Avinoam, 1937
 Language
 English.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2012.
 Physical description
 ix, 199 p. : ill ; 23 cm.
 Series
 London Mathematical Society lecture note series ; 395.
Access
Available online

Stacks

Unknown
QA174.2 .M366 2012

Unknown
QA174.2 .M366 2012
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. [187]194) and index.
 Contents

 Preface 1. Introduction 2. Some group theory 3. Groups of linear growth 4. The growth of nilpotent groups 5. The growth of soluble groups 6. Linear groups 7. Asymptotic cones 8. Groups of polynomial growth 9. Infinitely generated groups 10. Intermediate growth: Grigorchuk's first group 11. More groups of intermediate growth 12. Growth and amenability 13. Intermediate growth and residual finiteness 14. Explicit calculations 15. The generating function 16. The growth of free products 17. Conjugacy class growth Research problems References.
 (source: Nielsen Book Data)
 Publisher's Summary
 Growth of groups is an innovative new branch of group theory. This is the first book to introduce the subject from scratch. It begins with basic definitions and culminates in the seminal results of Gromov and Grigorchuk and more. The proof of Gromov's theorem on groups of polynomial growth is given in full, with the theory of asymptotic cones developed on the way. Grigorchuk's first and general groups are described, as well as the proof that they have intermediate growth, with explicit bounds, and their relationship to automorphisms of regular trees and finite automata. Also discussed are generating functions, groups of polynomial growth of low degrees, infinitely generated groups of local polynomial growth, the relation of intermediate growth to amenability and residual finiteness, and conjugacy class growth. This book is valuable reading for researchers, from graduate students onward, working in contemporary group theory.
(source: Nielsen Book Data)
Subjects
 Subject
 Group theory.
Bibliographic information
 Publication date
 2012
 Responsibility
 Avinoam Mann.
 Series
 London mathematical society lecture note series ; 395
 ISBN
 9781107657502
 1107657504