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Radicals of group algebras and permutation representations of symplectic groups

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Clarke, Robert John (1969) Radicals of group algebras and permutation representations of symplectic groups. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b1732838~S1

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Abstract

In part A we consider three separate problems concerned with the radical of the group algebra of a finite group over a field of characteristic p dividing the order of the group. In Section I we characterise group-theoretically those soluble groups for which the radical of the centre of the group algebra is an ideal of the group algebra. In Section II we find a canonical basis for the radical of the centre of the group algebra of a finite group. In Section III we give an algorithm for determining the radical of the group algebra of a p-soluble group. We evaluate the result for groups of p-Iength one and prove that the exponent of the radical in this case is the same as for a Sylow p-subgroup. We show by examples that no similar result holds in the general case.

In part B we quote a conjecture of J. A. Green's on characters of Chevalley groups and prove
 Theorem A (i) If the conjecture holds then, excepting for each r at most a finite number of values of q, the group PSp(2r+1,q) has no multiply transitive permutation representations for r > 1.
 (ii) PSp (4,q) has no multiply transitive permutation representations for q > 2, regardless of the conjecture.

Item Type: Thesis (PhD)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Algebra, Abstract, Finite groups, Permutations, Representations of groups, Symplectic groups
Official Date: 1969
Dates:
DateEvent
1969Submitted
Institution: University of Warwick
Theses Department: Mathematics Institute
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Green, J. A. (James Alexander)
Sponsors: Commonwealth Scholarship Commission (CSC) United Kingdom
Extent: 87 leaves
Language: eng

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