Profinite Graphs And Groups
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Profinite Graphs And Groups
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Author : Luis Ribes
language : en
Publisher: Springer
Release Date : 2017-08-23
Profinite Graphs And Groups written by Luis Ribes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-23 with Mathematics categories.
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.
Graphs Groups And Surfaces
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Author : A.T. White
language : en
Publisher: Elsevier
Release Date : 1985-01-01
Graphs Groups And Surfaces written by A.T. White and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-01-01 with Mathematics categories.
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing. Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'' and 9 as ``unsolved''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''.
Coverings Of Profinite Graphs
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Author : Amrita Acharyya
language : en
Publisher:
Release Date : 2013
Coverings Of Profinite Graphs written by Amrita Acharyya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Electronic dissertations categories.
We define a covering of a profinite graph to be a projective limit of a system of covering maps of finite graphs. With this notion of covering, we develop a covering theory for profinite graphs which is in many ways analogous to the classical theory of coverings of abstract graphs. For example, it makes sense to talk about the universal cover of a profinite graph and we show that it always exists and is unique. We define the profinite fundamental group of a profinite graph and show that a connected cover of a connected profinite graph is the universal cover if and only if its profinite fundamental group is trivial.
Cofinite Graphs And Their Profinite Completions
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Author : Bikash Chandra Das
language : en
Publisher:
Release Date : 2013
Cofinite Graphs And Their Profinite Completions written by Bikash Chandra Das and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Electronic dissertations categories.
We generalize the work of B. Hartley, to the category of topological graphs. The completion of a topological group in Hartley's work can be thought of as a particular example of the completion of a general uniform space. We consider topologies that are induced by uniformities, in order to topologize our graph structures and talk about their completions. In this dissertation generalize the idea of cofinite groups, due to B. Hartley. First we define cofinite spaces in general. Then, as a special case, we study cofinite graphs and their uniform completions. We are able to show that these completions are also cofinite graphs and being compact Hausdorff and totally disconnected they are rather regarded as profinite graphs. The idea of constructing a cofinite graph starts with defining a uniform topological graph in an appropriate fashion. We endow abstract graphs with uniformities corresponding to separating filter bases of equivalence relations with finitely many equivalence classes over the graph. By taking finitely many equivalence classes, we want to ensure the production of profinite structures over our topological graphs on taking the projective limit of the corresponding quotient graphs. It is established that for any cofinite graph there exists a unique cofinite completion. Generalizing Hartley's idea of cofinite groups and obtaining the structure for cofinite graphs we start establishing a parallel theory of cofinite graphs which in many ways can also be thought of as generalizations of the well-known works on pronite graphs by Pavel Zalesskii and Luis Ribes. Suitably defining the concept of cofinite connectedness of a cofinite graph we find that many of the properties of connectedness of topological spaces have analogs for cofinite connectedness. As an immediate consequence we obtain the following generalized characterization of the connected Cayley graphs of conite groups: G be a cofinite group, X be a cofinite space, then Cayley graph (G, X) is also cofinite graph and it is cofinitely connected if and only if X generates G (topologically). Our immediate next concern is developing group actions on cofinite graphs. Defining the action of an abstract group over a cofinite graph in the most natural way we are able to characterize a unique way of uniformizing an abstract group with a cofinite structure, obtained from the cofinite structure of the graph in the underlying action, so that the afore said action becomes uniformly continuous. We show that the aforesaid actions can actually be extended to the structures' of corresponding cofinite completions, preserving the underlying character of the original group action.
Groups Acting On Graphs
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Author : Warren Dicks
language : en
Publisher: Cambridge University Press
Release Date : 1989-03-09
Groups Acting On Graphs written by Warren Dicks and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-03-09 with Mathematics categories.
Originally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main three-dimensional topics are the equivariant loop and sphere theorems. The prerequisites grow as the book progresses up the dimensions. A familiarity with group theory is sufficient background for at least the first third of the book, while the later chapters occasionally state without proof and then apply various facts which require knowledge of homological algebra and algebraic topology. This book is essential reading for anyone contemplating working in the subject.
Profinite Groups
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Author : Luis Ribes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Profinite Groups written by Luis Ribes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
This self-contained book serves both as an introduction to profinite groups and as a reference for specialists in some areas of the theory. It contains complete and clear proofs for most results, many of which appear here in book form for the first time. Suitable as a basis for courses.
Geometric And Profinite Properties Of Groups
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Author : Owen Cotton-Barratt
language : en
Publisher:
Release Date : 2011
Geometric And Profinite Properties Of Groups written by Owen Cotton-Barratt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Amalgams categories.
Graphs Of Groups On Surfaces
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Author : A.T. White
language : en
Publisher: Elsevier
Release Date : 2001-04-27
Graphs Of Groups On Surfaces written by A.T. White and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-27 with Mathematics categories.
The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English church-bell music. The latter is facilitated by imbedding the right graph of the right group on an appropriate surface, with suitable symmetries. Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex. This is not as restrictive as it might sound; many developments in topological graph theory involve such imbeddings. The approach aims to make all this interconnected material readily accessible to a beginning graduate (or an advanced undergraduate) student, while at the same time providing the research mathematician with a useful reference book in topological graph theory. The focus will be on beautiful connections, both elementary and deep, within mathematics that can best be described by the intuitively pleasing device of imbedding graphs of groups on surfaces.
Ischia Group Theory 2008 Proceedings Of The Conference In Group Theory
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Author : Mariagrazia Bianchi
language : en
Publisher: World Scientific
Release Date : 2009-07-30
Ischia Group Theory 2008 Proceedings Of The Conference In Group Theory written by Mariagrazia Bianchi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-30 with Mathematics categories.
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.
New Horizons In Pro P Groups
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Author : Marcus du Sautoy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
New Horizons In Pro P Groups written by Marcus du Sautoy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.