Handbook of Computational Group Theory / Edition 1

Handbook of Computational Group Theory / Edition 1

ISBN-10:
1584883723
ISBN-13:
9781584883722
Pub. Date:
01/13/2005
Publisher:
Taylor & Francis
ISBN-10:
1584883723
ISBN-13:
9781584883722
Pub. Date:
01/13/2005
Publisher:
Taylor & Francis
Handbook of Computational Group Theory / Edition 1

Handbook of Computational Group Theory / Edition 1

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Overview

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 fundamental methods and algorithms in CGT presented at a level accessible even to advanced undergraduate students. It develops the theory of algorithms in full detail and highlights the connections between the different aspects of CGT and other areas of computer algebra. While acknowledging the importance of the complexity analysis of CGT algorithms, the authors' primary focus is on algorithms that perform well in practice rather than on those with the best theoretical complexity.

Throughout the book, applications of all the key topics and algorithms to areas both within and outside of mathematics demonstrate how CGT fits into the wider world of mathematics and science. The authors include detailed pseudocode for all of the fundamental algorithms, and provide detailed worked examples that bring the theorems and algorithms to life.

Product Details

ISBN-13: 9781584883722
Publisher: Taylor & Francis
Publication date: 01/13/2005
Series: Discrete Mathematics and Its Applications , #24
Edition description: New Edition
Pages: 530
Product dimensions: 6.12(w) x 9.19(h) x (d)

About the Author

Derek F. Holt, Bettina Eick, Eamonn A. O'Brien

Table of Contents

Group Theoretical Preliminaries. History of Computational Group Theory (CGT) and Its Place Within Computational Algebra. Methods of Representing Groups on a Computer. Base and Strong Generating Set Methods in Finite Permutation and Matrix Groups. Coset Enumeration. Computation in Finite Nilpotent and Solvable Groups. Representation Theory, Character Theory, and Cohomology. Algorithms Based on the Normal Structure of Finite Groups. Libraries and Databases of Groups. The Matrix Group Recognition Project. Special Techniques for Computing with Very Large Groups and Their Representations. Quotient Algorithms for Finitely Presented Groups. Rewriting Systems and the Knuth-Bendix Completion Process. Automatic Groups (Methods Involving Finite State Automata)
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