Applications Of Group Theory To Combinatorics

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Applications of Group Theory to Combinatorics

Jack Koolen,Jin Ho Kwak,Ming-Yao Xu
Applications of Group Theory to Combinatorics Book PDF

Author : Jack Koolen,Jin Ho Kwak,Ming-Yao Xu
Publisher : CRC Press
Page : 188 pages
File Size : 52,7 Mb
Release : 2008-07-02
Category : Mathematics
ISBN : 9780203885765

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Applications of Group Theory to Combinatorics by Jack Koolen,Jin Ho Kwak,Ming-Yao Xu Pdf

Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state

Combinatorial Group Theory

Roger C. Lyndon,Paul E. Schupp
Combinatorial Group Theory Book PDF

Author : Roger C. Lyndon,Paul E. Schupp
Publisher : Springer
Page : 354 pages
File Size : 49,6 Mb
Release : 2015-03-12
Category : Mathematics
ISBN : 9783642618963

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Combinatorial Group Theory by Roger C. Lyndon,Paul E. Schupp Pdf

From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews

Algebra VII

D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang
Algebra VII Book PDF

Author : D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 54,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642580130

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Algebra VII by D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang Pdf

From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996

Topics in Combinatorial Group Theory

Gilbert Baumslag
Topics in Combinatorial Group Theory Book PDF

Author : Gilbert Baumslag
Publisher : Birkhäuser
Page : 174 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885874

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Topics in Combinatorial Group Theory by Gilbert Baumslag Pdf

Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.

The History of Combinatorial Group Theory

B. Chandler,W. Magnus
The History of Combinatorial Group Theory Book PDF

Author : B. Chandler,W. Magnus
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394877

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The History of Combinatorial Group Theory by B. Chandler,W. Magnus Pdf

One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona ble choice as the object of a historical study.

Combinatorial and Geometric Group Theory

Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Combinatorial and Geometric Group Theory Book PDF

Author : Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 46,5 Mb
Release : 2011-01-28
Category : Mathematics
ISBN : 9783764399115

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Combinatorial and Geometric Group Theory by Oleg Bogopolski,Inna Bumagin,Olga Kharlampovich,Enric Ventura Pdf

This volume assembles several research papers in all areas of geometric and combinatorial group theory originated in the recent conferences in Dortmund and Ottawa in 2007. It contains high quality refereed articles developing new aspects of these modern and active fields in mathematics. It is also appropriate to advanced students interested in recent results at a research level.

Classical Topology and Combinatorial Group Theory

John Stillwell
Classical Topology and Combinatorial Group Theory Book PDF

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461243724

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Classical Topology and Combinatorial Group Theory by John Stillwell Pdf

In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.

Probabilistic Group Theory, Combinatorics, and Computing

Alla Detinko,Dane Flannery,Eamonn O'Brien
Probabilistic Group Theory Combinatorics and Computing Book PDF

Author : Alla Detinko,Dane Flannery,Eamonn O'Brien
Publisher : Springer
Page : 107 pages
File Size : 48,7 Mb
Release : 2013-01-13
Category : Mathematics
ISBN : 9781447148142

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Probabilistic Group Theory, Combinatorics, and Computing by Alla Detinko,Dane Flannery,Eamonn O'Brien Pdf

Probabilistic Group Theory, Combinatorics and Computing is based on lecture courses held at the Fifth de Brún Workshop in Galway, Ireland in April 2011. Each course discusses computational and algorithmic aspects that have recently emerged at the interface of group theory and combinatorics, with a strong focus on probabilistic methods and results. The courses served as a forum for devising new strategic approaches and for discussing the main open problems to be solved in the further development of each area. The book represents a valuable resource for advanced lecture courses. Researchers at all levels are introduced to the main methods and the state-of-the-art, leading up to the very latest developments. One primary aim of the book’s approach and design is to enable postgraduate students to make immediate use of the material presented.

Combinatorial and Geometric Group Theory

Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain
Combinatorial and Geometric Group Theory Book PDF

Author : Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 40,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821828229

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Combinatorial and Geometric Group Theory by Sean Cleary,Stephen Berman,Robert Gilman,Alexei G. Myasnikov,Vladimir Shpilrain Pdf

This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compact Riemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.

Combinatorial Group Theory

Wilhelm Magnus,Abraham Karrass,Donald Solitar
Combinatorial Group Theory Book PDF

Author : Wilhelm Magnus,Abraham Karrass,Donald Solitar
Publisher : Courier Corporation
Page : 466 pages
File Size : 51,7 Mb
Release : 2004-01-01
Category : Mathematics
ISBN : 9780486438306

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Combinatorial Group Theory by Wilhelm Magnus,Abraham Karrass,Donald Solitar Pdf

This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.

Handbook of Computational Group Theory

Derek F. Holt,Bettina Eick,Eamonn A. O'Brien
Handbook of Computational Group Theory Book PDF

Author : Derek F. Holt,Bettina Eick,Eamonn A. O'Brien
Publisher : CRC Press
Page : 532 pages
File Size : 48,7 Mb
Release : 2005-01-13
Category : Mathematics
ISBN : 9781420035216

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Handbook of Computational Group Theory by Derek F. Holt,Bettina Eick,Eamonn A. O'Brien Pdf

The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame

Algorithms and Classification in Combinatorial Group Theory

Gilbert Baumslag,Charles F. III Miller
Algorithms and Classification in Combinatorial Group Theory Book PDF

Author : Gilbert Baumslag,Charles F. III Miller
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397304

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Algorithms and Classification in Combinatorial Group Theory by Gilbert Baumslag,Charles F. III Miller Pdf

The papers in this volume are the result of a workshop held in January 1989 at the Mathematical Sciences Research Institute. Topics covered include decision problems, finitely presented simple groups, combinatorial geometry and homology, and automatic groups and related topics.

Groups, Combinatorics and Geometry

Martin W. Liebeck
Groups Combinatorics and Geometry Book PDF

Author : Martin W. Liebeck
Publisher : Cambridge University Press
Page : 505 pages
File Size : 41,5 Mb
Release : 1992-09-10
Category : Mathematics
ISBN : 9780521406857

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Groups, Combinatorics and Geometry by Martin W. Liebeck Pdf

This volume contains a collection of papers on the subject of the classification of finite simple groups.

Semigroups and Combinatorial Applications

Gerard Lallement
Semigroups and Combinatorial Applications Book PDF

Author : Gerard Lallement
Publisher : John Wiley & Sons
Page : 404 pages
File Size : 45,7 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015014357902

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Semigroups and Combinatorial Applications by Gerard Lallement Pdf

The purpose of this book is to present those parts of the theory of semigroups that are directly related to automata theory, algebraic linguistics, and combinatorics. Publications in these mathematical disciplines contained methods and results pertaining to the algebraic theory of semigroups, and this has contributed to considerable enrichment of the theory, enlargement of its scope, and improved its potential to become a major domain of algebra. Semigroup theory appears to provide a general framework for unifying and clarifying a number of topics in fields that at first sight appear unrelated. This book is intended as a textbook for graduate students in mathematics and computer science, and as a reference book for researchers interested in associative structures.

Combinatorial Group Theory and Topology

S. M. Gersten,John R. Stallings
Combinatorial Group Theory and Topology Book PDF

Author : S. M. Gersten,John R. Stallings
Publisher : Princeton University Press
Page : 564 pages
File Size : 43,8 Mb
Release : 1987-05-21
Category : Mathematics
ISBN : 9780691084107

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Combinatorial Group Theory and Topology by S. M. Gersten,John R. Stallings Pdf

Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah. Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.