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Author : Anonim
Publisher : American Mathematical Soc.
Page : 273 pages
File Size : 44,8 Mb
Release : 2006
Category : Combinatorial group theory
ISBN : 0821857517
Author : Benjamin Fine,Anthony M. Gaglione,Dennis Spellman
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 41,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839850
This volume consists of contributions by participants and speakers at two conferences. The first was entitled Combinatorial Group Theory, Discrete Groups and Number Theory and was held at Fairfield University, December 8-9, 2004. It was in honor of Professor Gerhard Rosenberger's sixtieth birthday. The second was the AMS Special Session on Infinite Group Theory held at Bard College, October 8-9, 2005. The papers in this volume provide a very interesting mix of combinatorial group theory, discrete group theory and ring theory as well as contributions to noncommutative algebraic cryptography.
Author : Gilbert Baumslag,Charles F. III Miller
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397304
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.
Author : Roger C. Lyndon,Paul E. Schupp
Publisher : Springer
Page : 354 pages
File Size : 45,7 Mb
Release : 2015-03-12
Category : Mathematics
ISBN : 9783642618963
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
Author : B. Chandler,W. Magnus
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394877
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.
Author : Gilbert Baumslag
Publisher : Birkhäuser
Page : 174 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885874
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.
Author : Benjamin Fine,Gerhard Rosenberger
Publisher : CRC Press
Page : 338 pages
File Size : 40,7 Mb
Release : 1999-07-27
Category : Mathematics
ISBN : 0824703197
A survey of one-relator products of cyclics or groups with a single defining relation, extending the algebraic study of Fuchsian groups to the more general context of one-relator products and related group theoretical considerations. It provides a self-contained account of certain natural generalizations of discrete groups.
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
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.
Author : Sean Cleary
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 46,6 Mb
Release : 2002
Category : Mathematics
ISBN : 9780821828229
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 compactRiemann 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.
Author : Valérie Berthé,Michel Rigo
Publisher : Birkhäuser
Page : 578 pages
File Size : 51,7 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783319691527
This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.
Author : Benjamin Fine
Publisher : Unknown
Page : 273 pages
File Size : 47,5 Mb
Release : 2006
Category : Electronic
ISBN : 0821839853
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
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.
Author : Benjamin Fine
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 51,7 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851166
Eighteen papers presented during a special AMS session designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results.
Author : D.J. Collins
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 49,5 Mb
Release : 1998-03-17
Category : Mathematics
ISBN : 3540637044
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
Author : Jack Koolen,Jin Ho Kwak,Ming-Yao Xu
Publisher : CRC Press
Page : 188 pages
File Size : 42,7 Mb
Release : 2008-07-02
Category : Mathematics
ISBN : 9780203885765
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