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Combinatorial Methods: Free Groups, Polynomials, and Free Algebras
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Vladimir Shpilrain, Alexander Mikhalev, Jie-Tai Yu
The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology at the beginning of the 20th Century. This book is divided into ...
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Classical Topology and Combinatorial Group Theory
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John Stillwell
This is a well-balanced introduction to topology that stresses geometric aspects. Focusing on historical background and visual interpretation of results, it emphasizes spaces with few dimensions, where visualization is possible, and interaction with combinatorial group theory via the fundamental group. It also present algorithms for topological ...
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Media Theory: Interdisciplinary Applied Mathematics
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David Eppstein, Jean-Claude Falmagne, Sergei Ovchinnikov
The focus of this book is a mathematical structure modeling a physical or biological system that can be in any of a number of 'states.' Each state is characterized by a set of binary features, and differs from some other neighbor state or states by just one of those feature. A simple example of a 'state' is a partial solution of a jigsaw puzzle, ...
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Algebraic Generalizations of Discrete Groups: A Path to Combinatorial Group Theory Through One-Relator Products
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Benjamin Fine, Gerhard Rosenberger
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.
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Combinatorial Group Theory and Applications to Geometry
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D. J. Collins, A. I. Kostrikin (Editor), I. R. Shafarevich (Editor)
"...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 ...
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Combinatorial group theory a topological approach
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Cohen
In this book, developed from courses taught at the University of London, the author aims to show the value of using topological methods in combinatorial group theory. The topological material is given in terms of the fundamental groupoid, giving results and proofs that are both stronger and simpler than the traditional ones. Several chapters deal ...
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Combinatorial Group Theory and Topology
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S M Gersten (Editor), John Robert Stallings
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Combinatorial Group Theory
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by
Roger C Lyndon
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. This includes a substantial and useful bibliography; (over 1100 (items))...the book is a valuable and welcome addition to the literature, ...
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Two-dimensional homotopy and combinatorial group theory
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Hog-Angeloni, Metzler, Sieradski
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 ...
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Combinatorial Group Testing and Its Appl
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by
Ding-Zhu Du, F K Hwang
Group testing has been used in medical, chemical and electrical testing, coding, drug screening, pollution control, multiaccess channel management, and more recently in data verification, clone library screening and AIDS testing. The mathematical model can be either combinatorial or probabilistic. This work is a summary of all important results ...
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Topics in combinatorial group theory
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by
Gilbert Baumslag
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 ...
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Computation with Finitely Presented Groups
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by
Sims
Research in computational group theory, an active subfield of computational algebra, has emphasized three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. It is the first text to present the fundamental algorithmic ideas which have been developed to compute with ...
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Combinatorial and geometric group theory Edinburgh, 1993
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by
Duncan, Gilbert, Howie 1953-
The contributed articles cover a wide range of topics in combinatorial and geometric group theory. It includes articles of current interest written by such scholars as S.M. Gersten, R.I. Grigorchuk, P.H. Kropholler, A Lubotsky, A.A. Razborov and E. Zelmanov.
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Papers on Group Theory and Topology
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by
Max Dehn
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Algorithms and Classification in Combinatorial Group Theory
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by
Gilbert Baumslag
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The History of Combinatorial Group Theory: A Case Study in the History of Ideas
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by
Wilhelm Magnus, Bruce Chandler
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Groups - Korea 1983: Proceedings of a Conference on Combinatorial Group Theory Held at Kyoungju, Korea, August 26-31, 1983
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by
A C Kim
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Algebra VII
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by
A N Parshin
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Computational Group Theory: Proceedings of the London Mathematical Society Symposium on Computational Group Theory
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Michael Atkinson (Editor)
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Combinatorial Group Theory: Proceedings of the Ams Special Session in Combinatorial Group Theory-Infinite Groups, April 23-24, 1988
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Bernard D. Fine (Editor), American Mathematical Society, Francis C. Y. Tang
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Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations
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by
Wilhelm Magnus
Classic account covers basic concepts: factor groups; Nielsen transformations; free and amalgamated products; commutator calculus. Revised 1975.
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Combinatorial and Geometric Group Theory: Ams Special Session, Combinatorial Group Theory, November 4-5, 2000, New York, New York: Ams Special Session, Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey
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by
Sean Cleary, Ph.D.
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 ...
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Handbook of Computational Group Theory
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by
Derek F Holt, Eick Bettina, O'Brien Eamonn
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 fundamental ...
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Groups - Korea 1983
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A C Kim (Editor), B H Neumann (Editor)
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Topology and Combinatorial Group Theory
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by
Paul Latiolais (Editor)
This book demonstrates the lively interaction between algebraic topology, very low dimensional topology and combinatorial group theory. Many of the ideas presented are still in their infancy, and it is hoped that the work here will spur others to new and exciting developments. Among the many techniques discussed are the use of obstruction groups ...
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