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# Ribes L. Profinite Graphs and Groups

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Springer International Publishing AG, 2017. — 473 p. — (A Series of Modern Surveys in Mathematics 66) — ISBN 978-3-319-61041-2.
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.
Preliminaries
Profinite Graphs
The Fundamental Group of a Profinite Graph
Profinite Groups Acting on $\mathcal{C}$ -Trees
Free Products of Pro- $\mathcal{C}$ Groups
Graphs of Pro- $\mathcal{C}$ Groups
Subgroups of Fundamental Groups of Graphs of Groups
Minimal Subtrees
Homology and Graphs of Pro- $\mathcal{C}$ Groups
The Virtual Cohomological Dimension of Profinite Groups
Separability Conditions in Free and Polycyclic Groups
Algorithms in Abstract Free Groups and Monoids
Abstract Groups vs Their Profinite Completions
Conjugacy in Free Products and in Free-by-Finite Groups
Conjugacy Separability in Amalgamated Products
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