Profinite Graphs And Groups
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Profinite Graphs and Groups
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.
New Horizons in pro-p Groups
Author: Marcus du Sautoy
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
A pro-p group is the inverse limit of some system of finite p-groups, that is, of groups of prime-power order where the prime - conventionally denoted p - is fixed. Thus from one point of view, to study a pro-p group is the same as studying an infinite family of finite groups; but a pro-p group is also a compact topological group, and the compactness works its usual magic to bring 'infinite' problems down to manageable proportions. The p-adic integers appeared about a century ago, but the systematic study of pro-p groups in general is a fairly recent development. Although much has been dis covered, many avenues remain to be explored; the purpose of this book is to present a coherent account of the considerable achievements of the last several years, and to point the way forward. Thus our aim is both to stimulate research and to provide the comprehensive background on which that research must be based. The chapters cover a wide range. In order to ensure the most authoritative account, we have arranged for each chapter to be written by a leading contributor (or contributors) to the topic in question. Pro-p groups appear in several different, though sometimes overlapping, contexts.
Ischia Group Theory 2008 - Proceedings Of The Conference In Group Theory
Author: Mariagrazia Bianchi
language: en
Publisher: World Scientific
Release Date: 2009-07-30
The volume contains a collection of research articles by leading experts in group theory, and reports of several accessible surveys of recent research in the area. The compilation provide an overview of the diversity of themes and applications that interest today's group theorists. The topics covered in this volume include: character theory, combinatorial group theory, varieties of groups, conjugacy classes, profinite groups, graphs connected with groups, subgroup structure, representation theory.