Combinatorial Group Theory

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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 : 44,5 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 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 : 47,9 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.

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 : 54,6 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.

Topics in Combinatorial Group Theory

Gilbert Baumslag
Topics in Combinatorial Group Theory Book PDF

Author : Gilbert Baumslag
Publisher : Birkhäuser
Page : 174 pages
File Size : 51,6 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.

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 : 41,9 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.

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 : 50,5 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

Daniel E. Cohen
Combinatorial Group Theory Book PDF

Author : Daniel E. Cohen
Publisher : Cambridge University Press
Page : 325 pages
File Size : 53,6 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.

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 : 52,9 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.

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 : 54,9 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.

Combinatorial Set Theory

Lorenz J. Halbeisen
Combinatorial Set Theory Book PDF

Author : Lorenz J. Halbeisen
Publisher : Springer
Page : 594 pages
File Size : 44,6 Mb
Release : 2017-12-20
Category : Mathematics
ISBN : 9783319602318

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Combinatorial Set Theory by Lorenz J. Halbeisen Pdf

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.

Groups, Graphs and Trees

John Meier
Groups Graphs and Trees Book PDF

Author : John Meier
Publisher : Cambridge University Press
Page : 244 pages
File Size : 55,7 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 0521895456

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Groups, Graphs and Trees by John Meier Pdf

This outstanding new book presents the modern, geometric approach to group theory, in an accessible and engaging approach to the subject. Topics include group actions, the construction of Cayley graphs, and connections to formal language theory and geometry. Theorems are balanced by specific examples such as Baumslag-Solitar groups, the Lamplighter group and Thompson's group. Only exposure to undergraduate-level abstract algebra is presumed, and from that base the core techniques and theorems are developed and recent research is explored. Exercises and figures throughout the text encourage the development of geometric intuition. Ideal for advanced undergraduates looking to deepen their understanding of groups, this book will also be of interest to graduate students and researchers as a gentle introduction to geometric group theory.

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 : 568 pages
File Size : 45,8 Mb
Release : 1987-05-21
Category : Mathematics
ISBN : 0691084106

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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.

Combinatorial Number Theory and Additive Group Theory

Alfred Geroldinger,Imre Ruzsa
Combinatorial Number Theory and Additive Group Theory Book PDF

Author : Alfred Geroldinger,Imre Ruzsa
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 47,9 Mb
Release : 2009-04-15
Category : Mathematics
ISBN : 9783764389611

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Combinatorial Number Theory and Additive Group Theory by Alfred Geroldinger,Imre Ruzsa Pdf

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Combinatorial and Geometric Group Theory

Sean Cleary
Combinatorial and Geometric Group Theory Book PDF

Author : Sean Cleary
Publisher : American Mathematical Soc.
Page : 292 pages
File Size : 44,6 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0821856324

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Combinatorial and Geometric Group Theory by Sean Cleary 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 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.

Combinatorial Group Testing and Its Applications

Dingzhu Du,Frank Hwang
Combinatorial Group Testing and Its Applications Book PDF

Author : Dingzhu Du,Frank Hwang
Publisher : World Scientific
Page : 337 pages
File Size : 41,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9789810241070

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Combinatorial Group Testing and Its Applications by Dingzhu Du,Frank Hwang Pdf

Group testing has been used in medical, chemical and electrical testing, coding, drug screening, pollution control, multiaccess channel management, and recently in data verification, clone library screening and AIDS testing. The mathematical model can be either combinatorial or probabilistic. This book summarizes all important results under the combinatorial model, and demonstrates their applications in real problems. Some other search problems, including the famous counterfeit-coins problem, are also studied in depth. There are two reasons for publishing a second edition of this book. The first is the usual need to update the text (after six years) and correct errors. The second -- and more important -- reason is to accommodate the recent sudden growth of interest in applying the idea of group testing to clone library screening. This development is much more than just a new application, since the new application brings with it new objectives which require a new twist of theory. It also embraces the growing importance of two topics: nonadaptive algorithms and error tolerance. Two new chapters, one on clone library screening and the other on error tolerance, have been added. Also included is a new chapter on counterfeit coins, the most famous search problem historically, which recently drew on an unexpected connection to some deep mathematical theory to yield new results. Finally, the chapters have been recognized into parts to provide focuses and perspectives.