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Author: Luis Ribes
Publisher: Springer Science & Business Media
ISBN: 3662040972
Category : Mathematics
Languages : en
Pages : 441
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Book Description
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.
Author: Luis Ribes
Publisher: Springer Science & Business Media
ISBN: 3662040972
Category : Mathematics
Languages : en
Pages : 441
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Book Description
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.
Author: John S. Wilson
Publisher: Clarendon Press
ISBN: 0191589217
Category : Mathematics
Languages : en
Pages : 302
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Book Description
This is the first book to be dedicated entirely to profinite groups, an area of algebra with important links to number theory and other areas of mathematics. It provides a comprehensive overview of the subject; prerequisite knowledge is kept to a minimum, and several major theorems are presented in an accessible form. The book would provide a valuable introduction for postgraduate students, or form a useful reference for researchers in other areas. The first few chapters lay the foundations and explain the role of profinite groups in number theory. Later chapters explore various aspects of profinite groups in more detail; these contain accessible and lucid accounts of many major theorems. Prerequisites are kept to a minimum with the basic topological theory summarized in an introductory chapter.
Author: Luis Ribes
Publisher: Springer
ISBN: 3319611992
Category : Mathematics
Languages : en
Pages : 471
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Book Description
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.
Author: Jorge Almeida
Publisher: Springer Nature
ISBN: 3030552152
Category : Mathematics
Languages : en
Pages : 278
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Book Description
This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.
Author: Stephen S. Shatz
Publisher: Princeton University Press
ISBN: 1400881854
Category : Mathematics
Languages : en
Pages : 264
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Book Description
In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present effectively that body of material upon which all modern research in Diophantine geometry and higher arithmetic is based, and to do so in a manner that emphasizes the many interesting lines of inquiry leading from these foundations.
Author: Stephen S. Shatz
Publisher: Princeton University Press
ISBN: 9780691080178
Category : Mathematics
Languages : en
Pages : 268
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Book Description
This volume reproduces, in the first five chapters, the content of a one semester course given at the University of Pennsylvania in the spring of 1968. The final chapter was material that was not presented during the course due to lack of time. The aim of the course was to acquaint students with a body of material upon which some of the modern research in Diophantine geometry and higher arithmetic is based, and in a way which emphasized the many interesting roads out of these elementary foundations.
Author: Marcus du Sautoy
Publisher: Springer Science & Business Media
ISBN: 9780817641719
Category : Mathematics
Languages : en
Pages : 444
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Book Description
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.
Author: J. D. Dixon
Publisher: Cambridge University Press
ISBN: 9780521542180
Category : Mathematics
Languages : en
Pages : 392
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Book Description
An up-to-date treatment of analytic pro-p groups for graduate students and researchers.
Author: H. Koch
Publisher: Springer Science & Business Media
ISBN: 9783540630036
Category : Mathematics
Languages : en
Pages : 280
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Book Description
From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians." Acta Scientiarum Mathematicarum, 1993
Author: Benjamin Klopsch
Publisher: Cambridge University Press
ISBN: 9781107005297
Category : Mathematics
Languages : en
Pages : 158
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Book Description
'In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.'
