Topics In Combinatorial Group Theory

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Topics in Combinatorial Group Theory

Gilbert Baumslag
Topics in Combinatorial Group Theory Book PDF

Author : Gilbert Baumslag
Publisher : Birkhäuser
Page : 174 pages
File Size : 52,9 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.

Combinatorial Group Theory

Daniel E. Cohen
Combinatorial Group Theory Book PDF

Author : Daniel E. Cohen
Publisher : CUP Archive
Page : 324 pages
File Size : 54,5 Mb
Release : 1989-08-17
Category : Mathematics
ISBN : 0521349362

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Combinatorial Group Theory by Daniel E. Cohen Pdf

In this book the author aims to show the value of using topological methods in combinatorial group theory.

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 : 47,9 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 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 : 41,8 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.

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 : 55,9 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

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 : 45,8 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

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 : 44,8 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.

Combinatorial Group Theory

Daniel E. Cohen
Combinatorial Group Theory Book PDF

Author : Daniel E. Cohen
Publisher : Cambridge University Press
Page : 325 pages
File Size : 47,5 Mb
Release : 1989-08-17
Category : Mathematics
ISBN : 9780521341332

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Combinatorial Group Theory by Daniel E. Cohen Pdf

In this book the author aims to show the value of using topological methods in combinatorial group theory.

Topics in Geometric Group Theory

Pierre de la Harpe
Topics in Geometric Group Theory Book PDF

Author : Pierre de la Harpe
Publisher : University of Chicago Press
Page : 320 pages
File Size : 47,8 Mb
Release : 2000-10-15
Category : Education
ISBN : 0226317196

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Topics in Geometric Group Theory by Pierre de la Harpe Pdf

In this book, Pierre de la Harpe provides a concise and engaging introduction to geometric group theory, a new method for studying infinite groups via their intrinsic geometry that has played a major role in mathematics over the past two decades. A recognized expert in the field, de la Harpe adopts a hands-on approach, illustrating key concepts with numerous concrete examples. The first five chapters present basic combinatorial and geometric group theory in a unique and refreshing way, with an emphasis on finitely generated versus finitely presented groups. In the final three chapters, de la Harpe discusses new material on the growth of groups, including a detailed treatment of the "Grigorchuk group." Most sections are followed by exercises and a list of problems and complements, enhancing the book's value for students; problems range from slightly more difficult exercises to open research problems in the field. An extensive list of references directs readers to more advanced results as well as connections with other fields.

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 : 54,5 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

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 : 40,8 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.

Topics in Groups and Geometry

Tullio Ceccherini-Silberstein,Michele D'Adderio
Topics in Groups and Geometry Book PDF

Author : Tullio Ceccherini-Silberstein,Michele D'Adderio
Publisher : Springer Nature
Page : 468 pages
File Size : 40,5 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030881092

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Topics in Groups and Geometry by Tullio Ceccherini-Silberstein,Michele D'Adderio Pdf

This book provides a detailed exposition of a wide range of topics in geometric group theory, inspired by Gromov’s pivotal work in the 1980s. It includes classical theorems on nilpotent groups and solvable groups, a fundamental study of the growth of groups, a detailed look at asymptotic cones, and a discussion of related subjects including filters and ultrafilters, dimension theory, hyperbolic geometry, amenability, the Burnside problem, and random walks on groups. The results are unified under the common theme of Gromov’s theorem, namely that finitely generated groups of polynomial growth are virtually nilpotent. This beautiful result gave birth to a fascinating new area of research which is still active today. The purpose of the book is to collect these naturally related results together in one place, most of which are scattered throughout the literature, some of them appearing here in book form for the first time. In this way, the connections between these topics are revealed, providing a pleasant introduction to geometric group theory based on ideas surrounding Gromov's theorem. The book will be of interest to mature undergraduate and graduate students in mathematics who are familiar with basic group theory and topology, and who wish to learn more about geometric, analytic, and probabilistic aspects of infinite groups.

Combinatorial Group Theory

Benjamin Fine,Anthony M. Gaglione
Combinatorial Group Theory Book PDF

Author : Benjamin Fine,Anthony M. Gaglione
Publisher : American Mathematical Soc.
Page : 191 pages
File Size : 55,8 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851166

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Combinatorial Group Theory by Benjamin Fine,Anthony M. Gaglione Pdf

The AMS Special Session on Combinatorial Group Theory--Infinite Groups, held at the University of Maryland in April 1988, was designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results. The session reflected the vitality and interests in infinite group theory, with eighteen speakers presenting lectures covering a wide range of group-theoretic topics, from purely logical questions to geometric methods. The heightened interest in classical combinatorial group theory was reflected in the sheer volume of work presented during the session. This book consists of eighteen papers presented during the session. Comprising a mix of pure research and exposition, the papers should be sufficiently understandable to the nonspecialist to convey a sense of the direction of this field. However, the volume will be of special interest to researchers in infinite group theory and combinatorial group theory, as well as to those interested in low-dimensional (especially three-manifold) topology.

Two-Dimensional Homotopy and Combinatorial Group Theory

Cynthia Hog-Angeloni,Wolfgang Metzler,Allan J. Sieradski
Two Dimensional Homotopy and Combinatorial Group Theory Book PDF

Author : Cynthia Hog-Angeloni,Wolfgang Metzler,Allan J. Sieradski
Publisher : Cambridge University Press
Page : 428 pages
File Size : 49,5 Mb
Release : 1993-12-09
Category : Mathematics
ISBN : 9780521447003

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Two-Dimensional Homotopy and Combinatorial Group Theory by Cynthia Hog-Angeloni,Wolfgang Metzler,Allan J. Sieradski Pdf

Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.

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 : 46,7 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.