How Groups Grow by Avinoam Mann
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.
'How Groups Grow is an excellent introduction to growth of groups for everybody interested in this subjectIt also touches a variety of adjacent subjects (such as amenability, isoperimetric inequalities, groups generated by automata, etc.) It is written in a very accessible style, with very clear exposition of all main results.' V. Nekrashevych, Bulletin of the American Mathematical Society
Avinoam Mann is a Professor Emeritus at his Alma Mater, the Einstein Institute of Mathematics in the Hebrew University of Jerusalem. He has published over a hundred papers on group theory and co-authored the influential book Analytic Pro-p Groups.
| SKU | Unavailable |
| ISBN 13 | 9781107657502 |
| ISBN 10 | 1107657504 |
| Title | How Groups Grow |
| Author | Avinoam Mann |
| Series | London Mathematical Society Lecture Note Series |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Cambridge University Press |
| Year published | 2011-12-15 |
| Number of pages | 210 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |