Group Theory, Combinatorics, and Computing
Group Theory, Combinatorics, and Computing

Author: Robert Fitzgerald Morse

Publisher: American Mathematical Soc.

Published: 2014-02-13

Total Pages: 202

ISBN-13: 0821894358

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This volume contains the proceedings of the International Conference on Group Theory, Combinatorics and Computing held from October 3-8, 2012, in Boca Raton, Florida. The papers cover a number of areas in group theory and combinatorics. Topics include finite simple groups, groups acting on structured sets, varieties of algebras, classification of groups generated by 3-state automata over a 2-letter alphabet, new methods for construction of codes and designs, groups with constraints on the derived subgroups of its subgroups, graphs related to conjugacy classes in groups, and lexicographical configurations. Application of computer algebra programs is incorporated in several of the papers. This volume includes expository articles on finite coverings of loops, semigroups and groups, and on the application of algebraic structures in the theory of communications. This volume is a valuable resource for researchers and graduate students working in group theory and combinatorics. The articles provide excellent examples of the interplay between the two areas.

Finite Simple Groups: Thirty Years of the Atlas and Beyond
Finite Simple Groups: Thirty Years of the Atlas and Beyond

Author: Manjul Bhargava

Publisher: American Mathematical Soc.

Published: 2017-07-24

Total Pages: 242

ISBN-13: 1470436787

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Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics. The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.

Investigations in Algebraic Theory of Combinatorial Objects
Investigations in Algebraic Theory of Combinatorial Objects

Author: I.A. Faradzev

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 513

ISBN-13: 9401719721

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X Köchendorffer, L.A. Kalu:lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed.

Designs and Their Codes
Designs and Their Codes

Author: E. F. Assmus

Publisher: Cambridge University Press

Published: 1994-01-06

Total Pages: 366

ISBN-13: 9780521458399

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A self-contained account suited for a wide audience describing coding theory, combinatorial designs and their relations.

Number Theory
Number Theory

Author: W.A. Coppel

Publisher: Springer Science & Business Media

Published: 2009-10-03

Total Pages: 620

ISBN-13: 0387894861

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Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.

Handbook of Computational Group Theory
Handbook of Computational Group Theory

Author: Derek F. Holt

Publisher: CRC Press

Published: 2005-01-13

Total Pages: 532

ISBN-13: 1420035215

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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

Low Rank Representations and Graphs for Sporadic Groups
Low Rank Representations and Graphs for Sporadic Groups

Author: Cheryl E. Praeger

Publisher: Cambridge University Press

Published: 1996-12-05

Total Pages: 157

ISBN-13: 0521567378

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This book presents a complete classification of the transitive permutation representations of rank at most five of the sporadic simple groups and their automorphism groups, together with a comprehensive study of the vertex-transitive graphs associated with these representations. Included is a list of all vertex-transitive, distance-regular graphs on which a sporadic almost simple group acts with rank at most five. In this list are some new, interesting distance-regular graphs of diameter two, which are not distance-transitive. For most of the representations a presentation of the sporadic group is given, with words in the given generators which generate a point stabiliser: this gives readers sufficient information to reconstruct and study the representations and graphs. Practical computational techniques appropriate for analysing finite vertex-transitive graphs are described carefully, making the book an excellent starting point for learning about groups and the graphs on which they act.

Design Theory: Volume 1
Design Theory: Volume 1

Author: Thomas Beth

Publisher: Cambridge University Press

Published: 1999-11-18

Total Pages: 730

ISBN-13: 9780521444323

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This is the first volume of the second edition of the standard text on design theory.