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.