**Author**: Roger C. Lyndon

**Publisher:** Springer

**ISBN:** 3642618960

**Category : **Mathematics

**Languages : **en

**Pages : **339

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**Book Description**
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**: Roger C. Lyndon

**Publisher:** Springer

**ISBN:** 3642618960

**Category : **Mathematics

**Languages : **en

**Pages : **339

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**Book Description**
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**: Wilhelm Magnus

**Publisher:** Courier Corporation

**ISBN:** 0486438309

**Category : **Mathematics

**Languages : **en

**Pages : **444

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**Book Description**
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**: B. Chandler

**Publisher:** Springer Science & Business Media

**ISBN:** 1461394872

**Category : **Mathematics

**Languages : **en

**Pages : **234

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**Book Description**
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:** BirkhĂ¤user

**ISBN:** 3034885873

**Category : **Mathematics

**Languages : **en

**Pages : **170

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**Book Description**
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**: Daniel E. Cohen

**Publisher:** Cambridge University Press

**ISBN:** 0521341337

**Category : **Mathematics

**Languages : **en

**Pages : **310

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

**Author**: Benjamin Fine

**Publisher:** American Mathematical Soc.

**ISBN:** 0821851160

**Category : **Mathematics

**Languages : **en

**Pages : **191

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**Book Description**
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.

**Author**: D.J. Collins

**Publisher:** Springer Science & Business Media

**ISBN:** 9783540637042

**Category : **Mathematics

**Languages : **en

**Pages : **240

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**Book Description**
This book consists of two parts. The first part provides a comprehensive description of that part of group theory which has its roots in topology. The second more advanced part deals with recent work on groups relating to topological manifolds. It is a valuable guide to research in this field. The text contains numerous examples, sketches of proofs and open problems.

**Author**: Gilbert Baumslag

**Publisher:** Springer Science & Business Media

**ISBN:** 1461397308

**Category : **Mathematics

**Languages : **en

**Pages : **232

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**Book Description**
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**: John Stillwell

**Publisher:** Springer Science & Business Media

**ISBN:** 1461243726

**Category : **Mathematics

**Languages : **en

**Pages : **336

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**Book Description**
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.

**Author**: Cynthia Hog-Angeloni

**Publisher:** Cambridge University Press

**ISBN:** 0521447003

**Category : **Mathematics

**Languages : **en

**Pages : **412

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**Book Description**
This book considers the current state of knowledge in the geometric and algebraic aspects of two-dimensional homotopy theory.