Profinite Graphs and Groups

Luis Ribes

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English

Springer Nature Switzerland AG
09 December 2018

Groups & group theory; Combinatorics & graph theory

Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

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.

By: Luis Ribes
Imprint: Springer Nature Switzerland AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2017
Volume: 66
Dimensions: Height: 235mm, Width: 155mm,
Weight: 741g
ISBN: 9783030104245
ISBN 10: 3030104249
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Pages: 471
Publication Date: 09 December 2018
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Profinite Graphs and Groups

The book has been written with great detail and clarity, so it can be easily read. ... This is one of a kind monograph that will be very useful for graduate students who are interested in profinite groups, as well as for specialists, as an excellent reference book. The book is a welcome contribution to the literature and will undoubtedly stimulate further development of the theory of profinite graphs and profinite groups. (Mikhail Kabenyuk, zbMATH 1457.20001, 2021) 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 reference for students and researchers in the field. (Primoz Moravec, Mathematical Reviews, 2018)