Profinite Graphs and Groups
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Beschreibung
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.
The first book to present a comprehensive treatment of profinite graphs, including applications to profinite and abstract groups Includes a complete proof of Serre's theorem on virtually free pro-p groups without torsion Contains appendices on abstract groups and automata theory Includes supplementary material: sn.pub/extras
Autor*in
Luis Ribes
Themen in »Profinite Graphs and Groups«
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
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“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 referencefor students and researchers in the field.” (Primož Moravec, Mathematical Reviews, 2018)
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