Computational Group Theory And The Theory Of Groups

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Handbook Of Computational Group Theory

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Author : Derek F. Holt
language : en
Publisher: CRC Press
Release Date : 2005-01-13

Handbook Of Computational Group Theory written by Derek F. Holt and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-13 with Mathematics categories.

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 fundame

Computational Group Theory And The Theory Of Groups

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Author : Luise-Charlotte Kappe
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Computational Group Theory And The Theory Of Groups written by Luise-Charlotte Kappe 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 2008 with Computers categories.

"The power of general purpose computational algebra systems running on personal computers has increased rapidly in recent years. For mathematicians doing research in group theory, this means a growing set of sophisticated computational tools are now available for their use in developing new theoretical results." "This volume consists of contributions by researchers invited to the AMS Special Session on Computational Group Theory held in March 2007. The main focus of the session was on the application of Computational Group Theory (CGT) to a wide range of theoretical aspects of group theory. The articles in this volume provide a variety of examples of how these computer systems helped to solve interesting theoretical problems within the discipline, such as constructions of finite simple groups, classification of $p$-groups via coclass, representation theory and constructions involving free nilpotent groups. The volume also includes an article by R. F. Morse highlighting applications of CGT in group theory and two survey articles." "Graduate students and researchers interested in various aspects of group theory will find many examples of Computational Group Theory helping research and will recognize it as yet another tool at their disposal."--BOOK JACKET.

Computational Group Theory And The Theory Of Groups Ii

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Author : Luise-Charlotte Kappe
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-04-08

Computational Group Theory And The Theory Of Groups Ii written by Luise-Charlotte Kappe 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 2010-04-08 with Mathematics categories.

This volume consists of contributions by researchers who were invited to the Harlaxton Conference on Computational Group Theory and Cohomology, held in August of 2008, and to the AMS Special Session on Computational Group Theory, held in October 2008. This volume showcases examples of how Computational Group Theory can be applied to a wide range of theoretical aspects of group theory. Among the problems studied in this book are classification of p-groups, covers of Lie groups, resolutions of Bieberbach groups, and the study of the lower central series of free groups. This volume also includes expository articles on the probabilistic zeta function of a group and on enumerating subgroups of symmetric groups. Researchers and graduate students working in all areas of Group Theory will find many examples of how Computational Group Theory helps at various stages of the research process, from developing conjectures through the verification stage. These examples will suggest to the mathematician ways to incorporate Computational Group Theory into their own research endeavors.

Computational Group Theory And The Theory Of Groups

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Author : Luise-Charlotte Kappe, Robert Fitzgerald Morse, Arturo Magidin
language : en
Publisher: American Mathematical Soc.
Release Date : 2008-10-03

Computational Group Theory And The Theory Of Groups written by Luise-Charlotte Kappe, Robert Fitzgerald Morse, Arturo Magidin 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 2008-10-03 with Computational complexity categories.

The power of general purpose computational algebra systems running on personal computers has increased rapidly in recent years. For mathematicians doing research in group theory, this means a growing set of sophisticated computational tools are now available for their use in developing new theoretical results. This volume consists of contributions by researchers invited to the AMS Special Session on Computational Group Theory held in March 2007. The main focus of the session was on the application of Computational Group Theory (CGT) to a wide range of theoretical aspects of group theory. The articles in this volume provide a variety of examples of how these computer systems helped to solve interesting theoretical problems within the discipline, such as constructions of finite simple groups, classification of $p$-groups via coclass, representation theory and constructions involving free nilpotent groups. The volume also includes an article by R. F. Morse highlighting applications of CGT in group theory and two survey articles. Graduate students and researchers interested in various aspects of group theory will find many examples of Computational Group Theory helping research and will recognize it as yet another tool at their disposal.

Applications Of The Theory Of Groups In Mechanics And Physics

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Author : Petre P. Teodorescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-04-30

Applications Of The Theory Of Groups In Mechanics And Physics written by Petre P. Teodorescu 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 2004-04-30 with Mathematics categories.

The notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc. This notion has developed during a century and this development is connected with the names of great mathematicians as E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S. Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In mathematics, as in other sciences, the simple and fertile ideas make their way with difficulty and slowly; however, this long history would have been of a minor interest, had the notion of group remained connected only with rather restricted domains of mathematics, those in which it occurred at the beginning. But at present, groups have invaded almost all mathematical disciplines, mechanics, the largest part of physics, of chemistry, etc. We may say, without exaggeration, that this is the most important idea that occurred in mathematics since the invention of infinitesimal calculus; indeed, the notion of group expresses, in a precise and operational form, the vague and universal ideas of regularity and symmetry. The notion of group led to a profound understanding of the character of the laws which govern natural phenomena, permitting to formulate new laws, correcting certain inadequate formulations and providing unitary and non contradictory formulations for the investigated phenomena.

Representation Theory Of Finite Groups

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Author : Benjamin Steinberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-23

Representation Theory Of Finite Groups written by Benjamin Steinberg 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 2011-10-23 with Mathematics categories.

This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.

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.

Applications Of Group Theory To Combinatorics

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Author : Jack Koolen
language : en
Publisher: CRC Press
Release Date : 2008-07-02

Applications Of Group Theory To Combinatorics written by Jack Koolen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-02 with Mathematics categories.

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

Computational Algebra And Number Theory

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Author : Wieb Bosma
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Computational Algebra And Number Theory written by Wieb Bosma 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 2013-03-09 with Mathematics categories.

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.

Group Based Cryptography

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Author : Alexei Myasnikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-17

Group Based Cryptography written by Alexei Myasnikov 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 2008-07-17 with Language Arts & Disciplines categories.

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory. Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far. Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.