Profinite graphs and groups / Luis Ribes.

Format:

Book

Author/Creator:

Ribes, Luis, author.

Series:

Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 66.

Ergebnisse der Mathematik und ihrer Grenzgebiete

Language:

English

Subjects (All):

Profinite groups.

Graph theory.

Physical Description:

xv, 471 pages : illustrations ; 25 cm.

Place of Publication:

Cham, Switzerland : Springer Nature, [2017].

Summary:

"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."--Provided by publisher.

Contents:

Profinite graphs

The fundamental group of a profinite graph

Profinite groups acting on C-trees

Free products of pro-C groups

Graphs of pro-C groups

Subgroups of fundamental groups of graphs of groups

Minimal subtrees

Homology and graphs of pro-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 amalgated products

Appendix A. Abstract graphs. Appendix B. Rational sets in free groups and automata.

Notes:

Includes bibliographical references (pages 453-459) and indexes.

Other Format:

Online version: Ribes, Luis. Profinite graphs and groups.

ISBN:

9783319610412

3319610414

OCLC:

988292423