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Finite primitive permutation groups of rank 4

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Vauhkonen-AK-1993-PhD-Thesis.pdfThesis2.77 MBAdobe PDFView/Open
Title: Finite primitive permutation groups of rank 4
Authors: Vauhkonen, Antti Kalervo
Item Type: Thesis or dissertation
Abstract: In this thesis we classify finite primitive permutation groups of rank 4. According to the 0' Nan-Scott theorem, a finite primitive permutation group is an affine group, an almost simple group, or has either simple diagonal action, product action or twisted wreath action. In Chapter 1 we completely determine the primitive rank 4 permutation groups with one of the last three types of actions up to permutation equivalence. In Chapter 2 we use Aschbacher's subgroup structure theorem for the finite classical groups to reduce the classification of affine primitive rank 4 permutation groups G of degree p*^ (p prime) to the case where a point stabilizer G in G satisfies soc(G/Z(G ))=L for some ^ 0 0 0 non-abelian simple group L. In Chapter 3 we classify all such groups G with L a simple group of Lie type over a finite field of characteristic p. Finally, in Chapter 4 we determine all the faithful primitive rank 4 permutation representations of the finite linear groups up to permutation equivalence.
Content Version: Open access
Date Awarded: 1993
URI: http://hdl.handle.net/10044/1/58543
Supervisor: Liebeck, Professor Martin W.
Sponsor/Funder: Osk. Huttunen Foundation
Department: Department of Mathematics
Publisher: Imperial College London
Qualification Level: Doctoral
Qualification Name: Doctor of Philosophy (PhD)
Author Permission: Permission granted
Appears in Collections:University of London awarded theses - Imperial authors



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