The affine primitive permutation groups of degree less than 1000.
type: Item
instance of: scholarly article
title: The affine primitive permutation groups of degree less than 1000.
zbMATH Open document ID: 1047.20005
DOI: 10.1016/S0747-7171(03)00031-2
author: Colva M. Roney-Dougal
author: W. R. Unger
published in: Journal of Symbolic Computation
publication date: 2003-08-19T00:00:00Z
review text: In this paper, the classification of the primitive permutation groups of degree less than \(1000\) is completed by determining the conjugacy classes of irreducible subgroups of \(\text{GL}(n,p)\) for a prime number \(p\) and \(p^n<1000\). Also the conjugacy classes of maximal subgroups of \(\text{GL}(8,2)\), \(\text{GL}(4,5)\) and \(\text{GL}(6,3)\) are determined. The results are based on the Dixon-Mortimer classification [\textit{J. D. Dixon} and \textit{B. Mortimer}, Math. Proc. Camb. Philos. Soc. 103, No. 2, 213-238 (1988; Zbl 0646.20003)] and \textit{M. Aschbacher}'s classification of maximal subgroups of \(\text{GL}(n,p)\) [Invent. Math. 76, 469-514 (1984; Zbl 0537.20023)]. They also rely heavily on several computer algebra systems like MAGMA and SMASH and on the algorithm \texttt{IrreducibleSubgroups}\(({\mathcal M}_1,{\mathcal M}_2)\) introduced by the authors. The given results include corrections of several errors in previous publications and databases.
Mathematics Subject Classification ID: 20B40
Mathematics Subject Classification ID: 20B10
Mathematics Subject Classification ID: 20B15
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20E28
zbMATH DE Number: 1967107
zbMATH Keywords: finite permutation groups
zbMATH Keywords: primitive groups
zbMATH Keywords: degrees
zbMATH Keywords: affine groups
zbMATH Keywords: irreducible groups
zbMATH Keywords: maximal subgroups
describes a project that uses: OEIS
describes a project that uses: PrimGrp
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 1967107