Permutation group algorithms

Akos Seress

264 pages, parution le 19/05/2003

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Résumé

Permutation group algorithms are one of the workhorses of symbolic algebra systems computing with groups. They played an indispensable role in the proof of many deep results, including the construction and study of sporadic finite simple groups.

This book describes the theory behind permutation group algorithms, up to the most recent developments based on the classification of finite simple groups. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout.

The central theme is the description of nearly linear time algorithms, which are extremely fast both in terms of asymptotic analysis and of practical running time.

A significant part of the permutation group library of the computational group algebra system GAP is based on nearly linear time algorithms. The book fills a significant gap in the symbolic computation literature.

It is recommended for everyone interested in using computers in group theory, and is suitable for advanced graduate courses.

Contents

Introduction
Black-box groups
Permutation groups: a complexity overview
Bases and strong generating sets
Further low-level algorithms
A library of nearly linear time algorithms
Solvable permutation groups
Strong generating tests
Backtrack methods
Large-base groups

Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Akos Seress
Parution	19/05/2003
Nb. de pages	264
Format	15,5 x 23,5
Couverture	Relié
Poids	535g
Intérieur	Noir et Blanc
EAN13	9780521661034
ISBN13	978-0-521-66103-4