The Todd Coxeter Coset Enumeration Algorithm For Finitely Generated Groups

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Computation with Finitely Presented Groups

Author : Charles C. Sims
Publisher : Cambridge University Press
ISBN 13 : 0521432138
Total Pages : 624 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Computation with Finitely Presented Groups by : Charles C. Sims

Download or read book Computation with Finitely Presented Groups written by Charles C. Sims and published by Cambridge University Press. This book was released on 1994-01-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.

Computational Algebra and Number Theory

Author : Wieb Bosma
Publisher : Springer Science & Business Media
ISBN 13 : 9401711089
Total Pages : 326 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Computational Algebra and Number Theory by : Wieb Bosma

Download or read book Computational Algebra and Number Theory written by Wieb Bosma and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Computational Group Theory

Author : Derek F. Holt
Publisher : CRC Press
ISBN 13 : 1420035215
Total Pages : 532 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Computational Group Theory by : Derek F. Holt

Download or read book Handbook of Computational Group Theory written by Derek F. Holt and published by CRC Press. This book was released on 2005-01-13 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Groups and Computation II

Author : Larry Finkelstein, William M. Kantor
Publisher : American Mathematical Soc.
ISBN 13 : 9780821885772
Total Pages : 404 pages
Book Rating : 4.8/5 (857 download)

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Book Synopsis Groups and Computation II by : Larry Finkelstein, William M. Kantor

Download or read book Groups and Computation II written by Larry Finkelstein, William M. Kantor and published by American Mathematical Soc.. This book was released on with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The workshop "Groups and Computations" took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms. Comments and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions. The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.

Combinatorial Group Theory

Author : Roger C. Lyndon
Publisher : Springer Science & Business Media
ISBN 13 : 9783540411581
Total Pages : 364 pages
Book Rating : 4.4/5 (115 download)

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Book Synopsis Combinatorial Group Theory by : Roger C. Lyndon

Download or read book Combinatorial Group Theory written by Roger C. Lyndon and published by Springer Science & Business Media. This book was released on 2001-01-12 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Computational Problems in Abstract Algebra

Author : John Leech
Publisher : Elsevier
ISBN 13 : 1483159426
Total Pages : 413 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Computational Problems in Abstract Algebra by : John Leech

Download or read book Computational Problems in Abstract Algebra written by John Leech and published by Elsevier. This book was released on 2014-05-17 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Problems in Abstract Algebra provides information pertinent to the application of computers to abstract algebra. This book discusses combinatorial problems dealing with things like generation of permutations, projective planes, orthogonal latin squares, graphs, difference sets, block designs, and Hadamard matrices. Comprised of 35 chapters, this book begins with an overview of the methods utilized in and results obtained by programs for the investigation of groups. This text then examines the method for establishing the order of a finite group defined by a set of relations satisfied by its generators. Other chapters describe the modification of the Todd–Coxeter coset enumeration process. This book discusses as well the difficulties that arise with multiplication and inverting programs, and of some ways to avoid or overcome them. The final chapter deals with the computational problems related to invariant factors in linear algebra. Mathematicians as well as students of algebra will find this book useful.

Groups St Andrews 2009 in Bath: Volume 1

Author : C. M. Campbell
Publisher : Cambridge University Press
ISBN 13 : 1139498274
Total Pages : 310 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Groups St Andrews 2009 in Bath: Volume 1 by : C. M. Campbell

Download or read book Groups St Andrews 2009 in Bath: Volume 1 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2011-06-16 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Gerhard Hiss and Volodymyr Nekrashevych, survey the latest developments in algebra.

Groups St Andrews 2001 in Oxford: Volume 1

Author : C. M. Campbell
Publisher : Cambridge University Press
ISBN 13 : 9781139437219
Total Pages : 316 pages
Book Rating : 4.4/5 (372 download)

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Book Synopsis Groups St Andrews 2001 in Oxford: Volume 1 by : C. M. Campbell

Download or read book Groups St Andrews 2001 in Oxford: Volume 1 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2003-11-06 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions from Marston Conder (Auckland), Persi Diaconis (Stanford) and Marcus Du Sautoy (Cambridge). The series of Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past twenty years. As with earlier volumes, these refereed volumes also contain accessible surveys of contemporary research fronts, as well as a diverse collection of short research articles. They form a valuable reference for researchers, especially graduate students, working in group theory.

Groups and Computation III

Author : William M. Kantor
Publisher : Walter de Gruyter
ISBN 13 : 3110872749
Total Pages : 376 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Groups and Computation III by : William M. Kantor

Download or read book Groups and Computation III written by William M. Kantor and published by Walter de Gruyter. This book was released on 2014-01-02 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions by the participants of the conference "Groups and Computation", which took place at The Ohio State University in Columbus, Ohio, in June 1999. This conference was the successor of two workshops on "Groups and Computation" held at DIMACS in 1991 and 1995. There are papers on permutation group algorithms, finitely presented groups, polycyclic groups, and parallel computation, providing a representative sample of the breadth of Computational Group Theory. On the other hand, more than one third of the papers deal with computations in matrix groups, giving an in-depth treatment of the currently most active area of the field. The points of view of the papers range from explicit computations to group-theoretic algorithms to group-theoretic theorems needed for algorithm development.

The Santa Cruz Conference on Finite Groups

Author : Bruce Cooperstein
Publisher : American Mathematical Soc.
ISBN 13 : 0821814400
Total Pages : 654 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Santa Cruz Conference on Finite Groups by : Bruce Cooperstein

Download or read book The Santa Cruz Conference on Finite Groups written by Bruce Cooperstein and published by American Mathematical Soc.. This book was released on 1980 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computing and Combinatorics

Author : Xiaodong Hu
Publisher : Springer Science & Business Media
ISBN 13 : 3540697322
Total Pages : 692 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Computing and Combinatorics by : Xiaodong Hu

Download or read book Computing and Combinatorics written by Xiaodong Hu and published by Springer Science & Business Media. This book was released on 2008-06-16 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refereed proceedings of the 14th Annual International Computing and Combinatorics Conference, COCOON 2008, held in Dalian, China, in June 2008. The 66 revised full papers presented were carefully reviewed and selected from 172 submissions. The papers are organized in topical sections on algorithms and data structures, algorithmic game theory and online algorithms, automata, languages, logic, and computability, combinatorics related to algorithms and complexity, complexity theory, cryptography, reliability and security, and database theory, computational biology and bioinformatics, computational algebra, geometry, and number theory, graph drawing and information visualization, graph theory and algorithms, communication networks, and optimization, wireless network, network optimization, and scheduling problem.

Handbook of Geometric Topology

Author : R.B. Sher
Publisher : Elsevier
ISBN 13 : 0080532853
Total Pages : 1145 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Geometric Topology by : R.B. Sher

Download or read book Handbook of Geometric Topology written by R.B. Sher and published by Elsevier. This book was released on 2001-12-20 with total page 1145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Topology is a foundational component of modern mathematics, involving the study of spacial properties and invariants of familiar objects such as manifolds and complexes. This volume, which is intended both as an introduction to the subject and as a wide ranging resouce for those already grounded in it, consists of 21 expository surveys written by leading experts and covering active areas of current research. They provide the reader with an up-to-date overview of this flourishing branch of mathematics.

Symmetric Generation of Groups

Author : Robert Curtis
Publisher : Cambridge University Press
ISBN 13 : 052185721X
Total Pages : 333 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Symmetric Generation of Groups by : Robert Curtis

Download or read book Symmetric Generation of Groups written by Robert Curtis and published by Cambridge University Press. This book was released on 2007-07-05 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive text which develops the notion of symmetric generation and applies the technique to sporadic simple groups.

Finitely Presented Groups

Author : Volker Diekert
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3111473570
Total Pages : 252 pages
Book Rating : 4.1/5 (114 download)

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Book Synopsis Finitely Presented Groups by : Volker Diekert

Download or read book Finitely Presented Groups written by Volker Diekert and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-10-07 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.

Some Tapas of Computer Algebra

Author : Arjeh M. Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 3662038919
Total Pages : 365 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Some Tapas of Computer Algebra by : Arjeh M. Cohen

Download or read book Some Tapas of Computer Algebra written by Arjeh M. Cohen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.

Groups St Andrews 2005: Volume 2

Author : C. M. Campbell
Publisher : Cambridge University Press
ISBN 13 : 0521694701
Total Pages : 443 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Groups St Andrews 2005: Volume 2 by : C. M. Campbell

Download or read book Groups St Andrews 2005: Volume 2 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2007-01-04 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected papers from 'Groups St Andrews 2005' cover a wide spectrum of modern group theory.

Finite Groups--coming of Age

Author : John McKay
Publisher : American Mathematical Soc.
ISBN 13 : 0821850474
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Finite Groups--coming of Age by : John McKay

Download or read book Finite Groups--coming of Age written by John McKay and published by American Mathematical Soc.. This book was released on 1985 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: These conference papers should dispel any post-classification pessimism about the future of the theory of finite simple groups. Having noted that the theory developed for the classification touches on so few other branches of mathematics, the editor focuses on research in finite simple groups not central to the classification and presents a broad context for the recent results in the field. The papers are aimed at researchers and graduate students in algebra. They pay special attention to current research in sporadic geometry, the Fischer-Griess Monster group, and moonshine. Though all the papers are of high research value, the following papers of unusual significance should be singled out: Frenkel, Lepowsky, and Meurman's construction of the Monster group $F_1$; Conway and Queen's computation of characters of $E_8({\bf C})$; Norton's proof of the uniqueness of the Monster; and Mason's exploration of moonshine.