Topics in Combinatorial Group Theory

Topics in Combinatorial Group Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 180
Release :
ISBN-10 : 3764329211
ISBN-13 : 9783764329211
Rating : 4/5 (11 Downloads)

Book Synopsis Topics in Combinatorial Group Theory by : Gilbert Baumslag

Download or read book Topics in Combinatorial Group Theory written by Gilbert Baumslag and published by Springer Science & Business Media. This book was released on 1993-09-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Combinatorial Group Theory
Author :
Publisher : Courier Corporation
Total Pages : 466
Release :
ISBN-10 : 9780486438306
ISBN-13 : 0486438309
Rating : 4/5 (06 Downloads)

Book Synopsis Combinatorial Group Theory by : Wilhelm Magnus

Download or read book Combinatorial Group Theory written by Wilhelm Magnus and published by Courier Corporation. This book was released on 2004-01-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The History of Combinatorial Group Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 240
Release :
ISBN-10 : 9781461394877
ISBN-13 : 1461394872
Rating : 4/5 (77 Downloads)

Book Synopsis The History of Combinatorial Group Theory by : B. Chandler

Download or read book The History of Combinatorial Group Theory written by B. Chandler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Geometric Group Theory

Topics in Geometric Group Theory
Author :
Publisher : University of Chicago Press
Total Pages : 320
Release :
ISBN-10 : 0226317196
ISBN-13 : 9780226317199
Rating : 4/5 (96 Downloads)

Book Synopsis Topics in Geometric Group Theory by : Pierre de la Harpe

Download or read book Topics in Geometric Group Theory written by Pierre de la Harpe and published by University of Chicago Press. This book was released on 2000-10-15 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Classical Topology and Combinatorial Group Theory

Classical Topology and Combinatorial Group Theory
Author :
Publisher : Springer Science & Business Media
Total Pages : 344
Release :
ISBN-10 : 9781461243724
ISBN-13 : 1461243726
Rating : 4/5 (24 Downloads)

Book Synopsis Classical Topology and Combinatorial Group Theory by : John Stillwell

Download or read book Classical Topology and Combinatorial Group Theory written by John Stillwell and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Combinatorial Group Theory

Topics in Combinatorial Group Theory
Author :
Publisher : Birkhäuser
Total Pages : 174
Release :
ISBN-10 : 9783034885874
ISBN-13 : 3034885873
Rating : 4/5 (74 Downloads)

Book Synopsis Topics in Combinatorial Group Theory by : Gilbert Baumslag

Download or read book Topics in Combinatorial Group Theory written by Gilbert Baumslag and published by Birkhäuser. This book was released on 2012-12-06 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Combinatorial Group Theory
Author :
Publisher : CUP Archive
Total Pages : 324
Release :
ISBN-10 : 0521349362
ISBN-13 : 9780521349369
Rating : 4/5 (62 Downloads)

Book Synopsis Combinatorial Group Theory by : Daniel E. Cohen

Download or read book Combinatorial Group Theory written by Daniel E. Cohen and published by CUP Archive. This book was released on 1989-08-17 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author aims to show the value of using topological methods in combinatorial group theory.