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Table of contents

  1. Front Matter
    Pages I-XV
  2. Luis Ribes
    Pages 1-26
  3. Basic Theory

    1. Front Matter
      Pages 27-28
    2. Luis Ribes
      Pages 29-61
    3. Luis Ribes
      Pages 177-219
  4. Applications to Profinite Groups

    1. Front Matter
      Pages 221-222
    2. Luis Ribes
      Pages 237-256
  5. Applications to Abstract Groups

  6. Back Matter
    Pages 429-471

About this book

Introduction

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.

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

Authors and affiliations

  • Luis┬áRibes
    • 1
  1. 1.School of Mathematics and StatisticsCarleton UniversityOttawaCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-61199-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-61041-2
  • Online ISBN 978-3-319-61199-0
  • Series Print ISSN 0071-1136
  • Series Online ISSN 2197-5655
  • Buy this book on publisher's site