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Computation With Finitely Presented Groups

Author: Charles C. Sims
Publisher: Cambridge University Press
ISBN: 9780521432139
Size: 40.15 MB
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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 Group Theory And The Theory Of Groups

Author: Luise-Charlotte Kappe
Publisher: American Mathematical Soc.
ISBN: 0821843656
Size: 63.67 MB
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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 Fibonacci Numbers

Author: Fredric T. Howard
Publisher: Springer Science & Business Media
ISBN: 9781402019388
Size: 44.37 MB
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This book contains 28 research articles from among the 49 papers and abstracts presented at the Tenth International Conference on Fibonacci Numbers and Their Applications. These articles have been selected after a careful review by expert referees, and they range over many areas of mathematics. The Fibonacci numbers and recurrence relations are their unifying bond. We note that the article "Fibonacci, Vern and Dan," which follows the Introduction to this volume, is not a research paper. It is a personal reminiscence by Marjorie Bicknell-Johnson, a longtime member of the Fibonacci Association. The editor believes it will be of interest to all readers. It is anticipated that this book, like the eight predecessors, will be useful to research workers and students at all levels who are interested in the Fibonacci numbers and their applications. March 16, 2003 The Editor Fredric T. Howard Mathematics Department Wake Forest University Box 7388 Reynolda Station Winston-Salem, NC 27109 xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Calvin Long, Chairman A. F. Horadam (Australia), Co-Chair Terry Crites A. N. Philippou (Cyprus), Co-Chair Steven Wilson A. Adelberg (U. S. A. ) C. Cooper (U. S. A. ) Jeff Rushal H. Harborth (Germany) Y. Horibe (Japan) M. Bicknell-Johnson (U. S. A. ) P. Kiss (Hungary) J. Lahr (Luxembourg) G. M. Phillips (Scotland) J. 'Thrner (New Zealand) xxiii xxiv LIST OF CONTRlBUTORS TO THE CONFERENCE * ADELBERG, ARNOLD, "Universal Bernoulli Polynomials and p-adic Congruences. " *AGRATINI, OCTAVIAN, "A Generalization of Durrmeyer-Type Polynomials. " BENJAMIN, ART, "Mathemagics.

Applied Finite Group Actions

Author: Adalbert Kerber
Publisher: Springer Science & Business Media
ISBN: 9783540659419
Size: 61.93 MB
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Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.

An Algebraic Introduction To K Theory

Author: Bruce A. Magurn
Publisher: Cambridge University Press
ISBN: 9780521800785
Size: 72.52 MB
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An introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra.

Combinatorial Matrix Theory

Author: Richard A. Brualdi
Publisher: Birkhäuser
ISBN: 3319709534
Size: 33.21 MB
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This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

Applied Cryptography And Network Security

Author: John Ioannidis
Publisher: Springer
Size: 56.55 MB
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This book constitutes the refereed proceedings of the Third International Conference on Applied Cryptography and Network Security, ACNS 2005, held in New York, NY, USA in June 2005. The 35 revised full papers presented were carefully reviewed and selected from 158 submissions. Among the topics covered are authentication, key exchange protocols, network denial of service, digital signatures, public key cryptography, MACs, forensics, intrusion detection, secure channels, identity-based encryption, network security analysis, DES, key extraction, homomorphic encryption, and zero-knowledge arguments.

Near Rings And Near Fields

Author: Yuen Fong
Publisher: Kluwer Academic Pub
ISBN: 9780792367062
Size: 55.87 MB
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The present volume contains the written version of three invited lectures and sixteen papers presented in the International Conference on Near-Rings and Near-Fields held in Stellenbosch, South Africa. These articles reflect contemporary research activities on the algebraic structure theory of near-rings and the interaction they have with group theory, geometry and combinatorics. Audience: This book will be of value to graduate students of mathematics and algebraists interested in all aspects of the near-ring theory.