Overview
- The first book to present a comprehensive treatment of profinite graphs, including applications to profinite and abstract groups
- Includes a complete proof of Serre's theorem on virtually free pro-p groups without torsion
- Contains appendices on abstract groups and automata theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 66)
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Table of contents (15 chapters)
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Front Matter
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Applications to Profinite Groups
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Front Matter
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Back Matter
Keywords
- profinite tree
- profinite group
- profinite graphs
- minimal subtrees
- free products of profinite groups
- free products of groups
- profinite topology
- virtual cohomological dimension
- separability conditions free groups
- separability conditions polycyclic groups
- conjugacy separability
- conjugacy classes product of groups
- product of subgroups
- topological groups
- geometric group theory
- homological methods group theory
- MSC 2010 20E18, 20E06, 20E08, 20F65, 20J05, 05C05, 20M35, 22C05
About this book
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject.
The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids.
Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open questions and suggestions for further reading.
Reviews
“The book systematically develops fundamentals of the theory of profinite graphs, with emphasis on exhibiting similarities with the Bass-Serre theory of abstract groups acting on abstract trees. As such, it provides a valuable referencefor students and researchers in the field.” (Primož Moravec, Mathematical Reviews, 2018)
Authors and Affiliations
Bibliographic Information
Book Title: Profinite Graphs and Groups
Authors: Luis Ribes
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-319-61199-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-61041-2Published: 01 September 2017
Softcover ISBN: 978-3-030-10424-5Published: 09 December 2018
eBook ISBN: 978-3-319-61199-0Published: 23 August 2017
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: XV, 471
Topics: Topological Groups, Lie Groups, Graph Theory, Group Theory and Generalizations