Computing chief series, composition series and socles in large permutation groups
type: Item
instance of: scholarly article
title: Computing chief series, composition series and socles in large permutation groups
zbMATH Open document ID: 0890.20006
author: Derek F. Holt
author: John J. Cannon
published in: Journal of Symbolic Computation
publication date: 1997-11-25T00:00:00Z
review text: This paper describes the theory and implementation of algorithms for computing chief series, composition series, and socles in large permutation groups. The authors are more concerned with the practical efficiency of the algorithm in actual computation than with the worst-case complexity (and they assume that the degree of the permutation group is not more than \(10^7\)), but they give references where most parts of the algorithm have been proven to be polynomial time. Most of their algorithms have been implemented in the Magma Computational Algebra System and the paper includes some tables of running time on various examples, showing that the algorithms can be practical on groups whose degree is in the hundreds of thousands. Several of the ideas involved are based on an algorithm of \textit{W. M. Kantor} [J. Symb. Comput. 12, No. 4/5, 517-526 (1991; Zbl 0792.20003)].
Mathematics Subject Classification ID: 20B40
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 20B35
zbMATH DE Number: 1077113
zbMATH Keywords: socles
zbMATH Keywords: composition factors
zbMATH Keywords: primitive permutation groups
zbMATH Keywords: algorithms
zbMATH Keywords: chief series
reviewed by: Albert J. Goodman
MaRDI profile type: Publication
OpenAlex ID: W1995566841
DOI: 10.1006/JSCO.1997.0127
description: scientific article; zbMATH DE number 1077113