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Topics in computational group theory relating to classifications of permutation groups
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Stratford, Benjamin Mark (2022) Topics in computational group theory relating to classifications of permutation groups. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3821786
Abstract
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].
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Permutation groups, Finite groups | ||||
Official Date: | January 2022 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Holt, Derek F. ; Capdeboscq, Inna | ||||
Format of File: | |||||
Extent: | 147 leaves : illustrations | ||||
Language: | eng |
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