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Topics in groups and geometry = grow...

Ceccherini-Silberstein, Tullio.

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Topics in groups and geometry = growth, amenability, and random walks /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Topics in groups and geometry/ by Tullio Ceccherini-Silberstein, Michele D'Adderio ; foreword by Efim Zelmanov.
Reminder of title:	growth, amenability, and random walks /
Author:	Ceccherini-Silberstein, Tullio.
other author:	D'Adderio, Michele.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xix, 464 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Geometric group theory. -
Online resource:	https://doi.org/10.1007/978-3-030-88109-2
ISBN:	9783030881092

Topics in groups and geometry = growth, amenability, and random walks /
Ceccherini-Silberstein, Tullio.

Topics in groups and geometrygrowth, amenability, and random walks /[electronic resource] :by Tullio Ceccherini-Silberstein, Michele D'Adderio ; foreword by Efim Zelmanov. - Cham :Springer International Publishing :2021. - xix, 464 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov's pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov's theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

ISBN: 9783030881092

Standard No.: 10.1007/978-3-030-88109-2doiSubjects--Topical Terms:

745240
Geometric group theory.

LC Class. No.: QA183 / .C43 2021

Dewey Class. No.: 512.2

Topics in groups and geometry = growth, amenability, and random walks /
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245 1 0 $a Topics in groups and geometry $h [electronic resource] : $b growth, amenability, and random walks / $c by Tullio Ceccherini-Silberstein, Michele D'Adderio ; foreword by Efim Zelmanov.
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300 $a xix, 464 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
520 $a This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov's pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov's theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.
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