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Topics in groups and geometrygrowth,...

Ceccherini-Silberstein, Tullio.

Topics in groups and geometrygrowth, amenability, and random walks /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Topics in groups and geometryby Tullio Ceccherini-Silberstein, Michele D'Adderio ; foreword by Efim Zelmanov.
其他題名:	growth, amenability, and random walks /
作者:	Ceccherini-Silberstein, Tullio.
其他作者:	D'Adderio, Michele.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xix, 464 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Geometric group theory.
電子資源:	https://doi.org/10.1007/978-3-030-88109-2
ISBN:	9783030881092$q(electronic bk.)

Topics in groups and geometrygrowth, 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$q(electronic bk.)

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

490173
Geometric group theory.

LC Class. No.: QA183 / .C43 2021

Dewey Class. No.: 512.2

Topics in groups and geometrygrowth, amenability, and random walks /
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