The affine primitive permutation groups of degree less than 1000.
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.
scientific article; zbMATH DE number 1967107
scientific article