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London Mathematical Society Lecture Note Series: How Groups Grow Series Number 395 (Paperback)
  • London Mathematical Society Lecture Note Series: How Groups Grow Series Number 395 (Paperback)
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London Mathematical Society Lecture Note Series: How Groups Grow Series Number 395 (Paperback)

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£44.99
Paperback 210 Pages / Published: 15/12/2011
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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 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.

Publisher: Cambridge University Press
ISBN: 9781107657502
Number of pages: 210
Weight: 320 g
Dimensions: 224 x 150 x 13 mm


MEDIA REVIEWS
'How Groups Grow is an excellent introduction to growth of groups for everybody interested in this subject. It 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
"The book gives an accessible account of group growth. It is very useful for different purposes such as in courses for advanced students, getting acquainted with the theory or learning about directions of research of the last decades." Wolfgang Woes, Mathematical Review
"How Groups Grow is an excellent introduction to growth of groups for everybody interested in this subject. It 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

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