How groups grow / Avinoam Mann.

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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...

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Bibliographic Details
Uniform Title:London Mathematical Society lecture note series ; 395.
Main Author: Mann, Avinoam, 1937- (Author)
Language:English
Published: Cambridge : Cambridge University Press, 2012.
Series:London Mathematical Society lecture note series ; 395.
Subjects:
Group theory.
Online Access:
Connect to online resource - MSU authorized users (Digital Object Identifier Permalink)
Physical Description:1 online resource (ix, 199 pages) : digital, PDF file(s).
Format: Electronic eBook

MARC

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490 1 |a London Mathematical Society lecture note series ;  |v 395 
500 |a Title from publisher's bibliographic system (viewed on 05 Oct 2015). 
505 0 0 |g 1  |t Introduction  |g 1 --  |g 2  |t Some Group Theory  |g 15 --  |g 2.1  |t Finite Index Subgroups  |g 15 --  |g 2.2  |t Growth  |g 18 --  |g 2.3  |t Soluble and Polycyclic Groups  |g 25 --  |g 2.4  |t Nilpotent Groups  |g 27 --  |g 2.5  |t Isoperimetric Inequalities  |g 32 --  |g 3  |t Groups of Linear Growth  |g 36 --  |g 3.1  |t Linear Growth  |g 36 --  |g 3.2  |t Linear Growth Functions  |g 41 --  |g 4  |t The Growth of Nilpotent Groups  |g 44 --  |g 4.1  |t Polynomial Growth of Nilpotent Groups  |g 44 --  |g 4.2  |t Groups of Small Degree  |g 50 --  |g 5  |t The Growth of Soluble Groups  |g 56 --  |g 5.1  |t Soluble Groups of Polynomial Growth  |g 56 --  |g 5.2  |t Uniform Exponential Growth of Soluble Groups  |g 60 --  |g 6  |t Linear Groups  |g 63 --  |g 7  |t Asymptotic Cones  |g 67 --  |g 8  |t Groups of Polynomial Growth  |g 77 --  |g 9  |t Infinitely Generated Groups  |g 81 --  |g 10  |t Intermediate Growth: Grigorchuk's First Group  |g 90 --  |g 11  |t More Groups of Intermediate Growth  |g 108 --  |g 11.1  |t The General Grigorchuk Groups  |g 108 --  |g 11.2  |t Groups Acting on Regular Trees  |g 113 --  |g 11.3  |t Groups Defined by Finite Automata  |g 115 --  |g 11.4  |t Bartholdi-Erschler Groups  |g 119 --  |g 12  |t Growth and Amenability  |g 121 --  |g 12.1  |t Amenability and Intermediate Growth  |g 121 --  |g 12.2tMore Isoperimetric Inequalities  |g 127 --  |g 13  |t Intermediate Growth and Residual Finiteness  |g 131 --  |g 14  |t Explicit Calculations  |g 136 --  |g 14.1  |t The Trefoil Group  |g 136 --  |g 14.2  |t Wreath Products  |g 139 --  |g 14.3  |t Free Products with Amalgamations and HNN-Extensions  |g 141 --  |g 14.4  |t Central Products  |g 146 --  |g 15  |t The Generating Function  |g 148 --  |g 16  |t The Growth of Free Products  |g 158 --  |g 17  |t Conjugacy Growth  |g 176 --  |g 18  |t Research Problems  |g 185. 
520 |a 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. 
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