Automorphism group computation and isomorphism testing in finite groups
type: Item
instance of: scholarly article
title: Automorphism group computation and isomorphism testing in finite groups
zbMATH Open document ID: 1032.20016
DOI: 10.1016/S0747-7171(02)00133-5
author: John J. Cannon
author: Derek F. Holt
published in: Journal of Symbolic Computation
publication date: 2003-08-17T00:00:00Z
review text: The authors generalize the automorphism group algorithm of \textit{E. A. O'Brien} [Computational algebra and number theory. Math. Appl., Dordr. 325, 83-90 (1995; Zbl 0836.20002)] and \textit{M. J. Smith} [Thesis, Australian National University (1994)] to the case of nonsolvable groups: Automorphisms of the radical factor are obtained via the normalizer in a suitable permutation representation. Then automorphisms are lifted along a characteristic series, similar to the approach of \textit{J. J. Cannon, B. C. Cox} and \textit{D. F. Holt} [J. Symb. Comput. 31, No. 1-2, 149-161 (2001; Zbl 0984.20002)] for subgroups. By choosing a particular characteristic series the authors are able to simplify the calculation of compatible pairs. The test for automorphisms that lift is performed by a backtrack search in a suitable permutation representation. The paper closes with an investigation of the algorithm's performance. The worst case is that of \(p\)-groups, for which an improved algorithm recently has been proposed by \textit{B. Eick, C. R. Leedham-Green} and \textit{E. A. O'Brien} [Commun. Algebra 30, No. 5, 2271-2295 (2002; Zbl 1006.20001)].
reviewed by: A. Hulpke
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20B40
Mathematics Subject Classification ID: 20-04
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 1965167
zbMATH Keywords: permutation groups
zbMATH Keywords: algorithms
zbMATH Keywords: automorphism groups
zbMATH Keywords: isomorphism testing
describes a project that uses: Magma
describes a project that uses: GAP
describes a project that uses: Cayley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1965167