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GLNormaliser.zipAlgorithm code & test cases33.65 kBZIPView/Open
HannahCouttsPhDThesis.pdfThesis text946.71 kBAdobe PDFView/Open
Title: Topics in computational group theory : primitive permutation groups and matrix group normalisers
Authors: Coutts, Hannah Jane
Supervisors: Roney-Dougal, Colva Mary
Issue Date: Nov-2011
Abstract: Part I of this thesis presents methods for finding the primitive permutation groups of degree d, where 2500 ≤ d < 4096, using the O'Nan-Scott Theorem and Aschbacher's theorem. Tables of the groups G are given for each O'Nan-Scott class. For the non-affine groups, additional information is given: the degree d of G, the shape of a stabiliser in G of the primitive action, the shape of the normaliser N in S[subscript(d)] of G and the rank of N. Part II presents a new algorithm NormaliserGL for computing the normaliser in GL[subscript(n)](q) of a group G ≤ GL[subscript(n)](q). The algorithm is implemented in the computational algebra system MAGMA and employs Aschbacher's theorem to break the problem into several cases. The attached CD contains the code for the algorithm as well as several test cases which demonstrate the improvement over MAGMA's existing algorithm.
Type: Thesis
Publisher: University of St Andrews
Appears in Collections:Pure Mathematics Theses

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