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Profinite graphs and groups

Ribes, Luis.

Profinite graphs and groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Profinite graphs and groupsby Luis Ribes.
Author:	Ribes, Luis.
Published:	Cham :Springer International Publishing :2017.
Description:	xv, 471 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Profinite groups.
Online resource:	http://dx.doi.org/10.1007/978-3-319-61199-0
ISBN:	9783319611990$q(electronic bk.)

Profinite graphs and groups
Ribes, Luis.

Profinite graphs and groups[electronic resource] /by Luis Ribes. - Cham :Springer International Publishing :2017. - xv, 471 p. :ill., digital ;24 cm. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics,v.660071-1136 ;. - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics ;v.65..

1 Preliminaries -- Part I Basic Theory -- 2 Profinite Graphs -- 3 The Fundamental Group of a Profinite Graph -- 4 Profinite Groups Acting on C-Trees -- 5 Free Products of Pro-C Groups -- 6 Graphs of Pro-C Groups -- Part II Applications to Profinite Groups -- 7 Subgroups of Fundamental Groups of Graphs of Groups -- 8 Minimal Subtrees -- 9 Homology and Graphs of Pro-C Groups -- 10 The Virtual Cohomological Dimension of Profinite Groups -- Part III Applications to Abstract Groups -- 11 Separability Conditions in Free and Polycyclic Groups -- 12 Algorithms in Free Groups and Monoids -- 13 Abstract Groups vs their Profinite Completions -- 14 Conjugacy in Free Products and in Free-by-finite Groups -- 15 Conjugacy Separability in Amalgamated Products -- Appendix A Abstract Graphs -- Appendix B Rational Sets in Free Groups and Automata -- Bibliography -- Index.

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.

ISBN: 9783319611990$q(electronic bk.)

Standard No.: 10.1007/978-3-319-61199-0doiSubjects--Topical Terms:

466543
Profinite groups.

LC Class. No.: QA174.2 / .R53 2017

Dewey Class. No.: 512.2

Profinite graphs and groups
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245 1 0 $a Profinite graphs and groups $h [electronic resource] / $c by Luis Ribes.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2017.
300 $a xv, 471 p. : $b ill., digital ; $c 24 cm.
490 1 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics, $x 0071-1136 ; $v v.66
505 0 $a 1 Preliminaries -- Part I Basic Theory -- 2 Profinite Graphs -- 3 The Fundamental Group of a Profinite Graph -- 4 Profinite Groups Acting on C-Trees -- 5 Free Products of Pro-C Groups -- 6 Graphs of Pro-C Groups -- Part II Applications to Profinite Groups -- 7 Subgroups of Fundamental Groups of Graphs of Groups -- 8 Minimal Subtrees -- 9 Homology and Graphs of Pro-C Groups -- 10 The Virtual Cohomological Dimension of Profinite Groups -- Part III Applications to Abstract Groups -- 11 Separability Conditions in Free and Polycyclic Groups -- 12 Algorithms in Free Groups and Monoids -- 13 Abstract Groups vs their Profinite Completions -- 14 Conjugacy in Free Products and in Free-by-finite Groups -- 15 Conjugacy Separability in Amalgamated Products -- Appendix A Abstract Graphs -- Appendix B Rational Sets in Free Groups and Automata -- Bibliography -- Index.
520 $a 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.
650 0 $a Profinite groups. $3 466543
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Topological Groups, Lie Groups. $3 273787
650 2 4 $a Graph Theory. $3 522732
650 2 4 $a Group Theory and Generalizations. $3 274819
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830 0 $a Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A series of modern surveys in mathematics ; $v v.65. $3 776013
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-61199-0
950 $a Mathematics and Statistics (Springer-11649)