Topics In Group Theory
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Topics In Group Theory
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Author : Geoff Smith
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-05-15
Topics In Group Theory written by Geoff Smith and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-15 with Mathematics categories.
The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed for readers approaching the subject for the first time, this book reviews all the essentials. It recaps the basic definitions and results, including Lagranges Theorem, the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" demonstrates an assortment of results that can be achieved with the theoretical machinery.
Topics In Group Theory
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Author : Geoff Smith
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topics In Group Theory written by Geoff Smith and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
We very much hope that this book will be read by the interested student (and not just be parked on a shelf for occasional consultation). If you want a comprehensive reference book on Group Theory, do not buy this text. There are much better books available, some of which are mentioned below. We have a tale to tell; the absolute essentials of the theory of groups, followed by some entertainments and some more advanced material. The theory of groups is an enormous body of material which interacts with other branches of mathematics at countless frontiers. Some parts of the theory are essentially complete, but in other areas all we see are questions. People happily read novels, so why not mathematics books? When math ematics was studied by only a few people, there was less need to try to write attractively or encouragingly since the likely readership consisted of a small group of highly motivated individuals who needed little encouragement. Even so, many talented academic writers managedto write brilliantly because they knew no other way. As higher education has opened up in economically devel oped countries, a much more diverse collection of people is exploring advanced mathematics and science. The challenge for authors is to produce books which engage this wider community without compromising the content.
Topics In Geometric Group Theory
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Author : Pierre de la Harpe
language : en
Publisher: University of Chicago Press
Release Date : 2000-10-15
Topics In Geometric Group Theory written by Pierre de la Harpe and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-10-15 with Education categories.
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.
Topics In The Theory Of Group Presentations
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Author : D. L. Johnson
language : en
Publisher: Cambridge University Press
Release Date : 1980-07-31
Topics In The Theory Of Group Presentations written by D. L. Johnson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-07-31 with Mathematics categories.
These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.
Problems In Group Theory
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Author : John D. Dixon
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Problems In Group Theory written by John D. Dixon and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
265 challenging problems in all phases of group theory, gathered for the most part from papers published since 1950, although some classics are included.
Visual Group Theory
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Author : Nathan Carter
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-08
Visual Group Theory written by Nathan Carter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-08 with Education categories.
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.
Lectures On Profinite Topics In Group Theory
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Author : Benjamin Klopsch
language : en
Publisher: Cambridge University Press
Release Date : 2011-02-10
Lectures On Profinite Topics In Group Theory written by Benjamin Klopsch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-10 with Mathematics categories.
'In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first introduces the theory of compact p-adic Lie groups. The second explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.'
Fundamentals Of Group Theory
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Author : Steven Roman
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-26
Fundamentals Of Group Theory written by Steven Roman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-26 with Mathematics categories.
Fundamentals of Group Theory provides a comprehensive account of the basic theory of groups. Both classic and unique topics in the field are covered, such as an historical look at how Galois viewed groups, a discussion of commutator and Sylow subgroups, and a presentation of Birkhoff’s theorem. Written in a clear and accessible style, the work presents a solid introduction for students wishing to learn more about this widely applicable subject area. This book will be suitable for graduate courses in group theory and abstract algebra, and will also have appeal to advanced undergraduates. In addition it will serve as a valuable resource for those pursuing independent study. Group Theory is a timely and fundamental addition to literature in the study of groups.
A First Course In Group Theory
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Author : Bijan Davvaz
language : en
Publisher: Springer Nature
Release Date : 2021-11-10
A First Course In Group Theory written by Bijan Davvaz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-10 with Mathematics categories.
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. Topics on important examples of groups (like cyclic groups, permutation groups, group of arithmetical functions, matrix groups and linear groups), Lagrange’s theorem, normal subgroups, factor groups, derived subgroup, homomorphism, isomorphism and automorphism of groups have been discussed in depth. Covering all major topics, this book is targeted to undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Topological Methods In Group Theory
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Author : Ross Geoghegan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-17
Topological Methods In Group Theory written by Ross Geoghegan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-17 with Mathematics categories.
This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.