Topics in computational group theory relating to classifications of permutation groups

In this thesis we extend the classification of primitive permutation groups of degree d to include 4096 ≤ d < 8192. We make heavy use of the O'Nan-Scott Theorem, Aschbacher's Theorem for general linear groups, and the Classification of the Finite Simple Groups. We follow the method give...

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Bibliographic Details
Main Author Stratford, Benjamin Mark
Format Dissertation
LanguageEnglish
Published University of Warwick 2022
Subjects
QA Mathematics
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Summary:In this thesis we extend the classification of primitive permutation groups of degree d to include 4096 ≤ d < 8192. We make heavy use of the O'Nan-Scott Theorem, Aschbacher's Theorem for general linear groups, and the Classification of the Finite Simple Groups. We follow the method given in [13] making the necessary changes and computations. This work required the construction of a deterministic test which outputs whether a subgroup of GL(d,q) is semilinear. We have also produced a general function which, for a given 1 ≤ d ≤ 1000000, outputs all non-afine primitive groups of degree d. Finally we have classified the quasiprimitive groups up to degree 3600, making use of Praeger's "O'Nan-Scott Theorem" for quasiprimitive groups given in [33].
Bibliography:0000000509697147