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Topics in Groups and Geometry = Growth, Amenability, and Random Walks /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Topics in Groups and Geometry/ by Tullio Ceccherini-Silberstein, Michele D'Adderio.
其他題名:	Growth, Amenability, and Random Walks /
作者:	Ceccherini-Silberstein, Tullio.
其他作者:	D'Adderio, Michele.
面頁冊數:	XIX, 464 p. 30 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Graph Theory. -
電子資源:	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. - 1st ed. 2021. - XIX, 464 p. 30 illus.online resource. - Springer Monographs in Mathematics,2196-9922. - Springer Monographs in Mathematics,.

- Foreword -- Preface -- Part I Algebraic Theory: 1. Free Groups -- 2. Nilpotent Groups -- 3. Residual Finiteness and the Zassenhaus Filtration -- 4. Solvable Groups -- 5. Polycyclic Groups -- 6. The Burnside Problem -- Part II Geometric Theory: 7. Finitely Generated Groups and Their Growth Functions -- 8. Hyperbolic Plane Geometry and the Tits Alternative -- 9. Topological Groups, Lie Groups, and Hilbert Fifth Problem -- 10. Dimension Theory -- 11. Ultraﬁlters, Ultraproducts, Ultrapowers, and Asymptotic Cones -- 12. Gromov’s Theorem -- Part III Analytic and Probabilistic Theory: 13. The Theorems of Polya and Varopoulos -- 14. Amenability, Isoperimetric Proﬁle, and Følner Functions -- 15. Solutions or Hints to Selected Exercises -- References -- Subject Index -- Index of Authors.

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:

786670
Graph Theory.

LC Class. No.: QA174-183

Dewey Class. No.: 512.2

Topics in Groups and Geometry = Growth, Amenability, and Random Walks /
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