Dixon's character table algorithm revisited
type: Item
instance of: scholarly article
title: Dixon's character table algorithm revisited
zbMATH Open document ID: 0701.20002
DOI: 10.1016/S0747-7171(08)80077-6
author: Gerhard J. A. Schneider
published in: Journal of Symbolic Computation
publication date: 1990-01-01T00:00:00Z
review text: In 1967 the reviewer described an algorithm for computing the ordinary characters of a finite group from the class matrices using finite fields [\textit{J. D. Dixon}, Numer. Math. 10, 446-450 (1967; Zbl 0166.29002)], and an implementation of this algorithm has been available to users of the group theory system CAYLEY. In the present paper the author describes modifications to the algorithm which reduce the number of (expensive) computations of the class matrices. These produce dramatic improvements in the running time. The algorithm is still only useful for groups with relatively small order or with relatively few conjugacy classes. However, examples given show that the 12 characters of the Mathieu group \(M(22)\) could be computed in 563 seconds, and the 88 characters of the Burnside group \(B(2,4)\) of order \(2^{12}\) could be computed in 87 seconds. The modified algorithm is implemented in the current version of CAYLEY.
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20-04
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 20C34
zbMATH DE Number: 4148390
zbMATH Keywords: ordinary characters
zbMATH Keywords: finite group
zbMATH Keywords: class matrices
zbMATH Keywords: CAYLEY
zbMATH Keywords: running time
zbMATH Keywords: Mathieu group \(M(22)\)
zbMATH Keywords: Burnside group
zbMATH Keywords: modified algorithm
describes a project that uses: Cayley
describes a project that uses: CAS
MaRDI profile type: Publication
cites work: Q3333220
cites work: Q4145881
cites work: High speed computation of group characters
cites work: Q4103728
cites work: Q5619223
cites work: Q3337625
cites work: Computing character degrees in p-groups
full work available at URL: s0747-7171(08)80077-6
OpenAlex ID: W1967540202
description: scientific article; zbMATH DE number 4148390