Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.594878
Title: Radicals of group algebras and permutation representations of symplectic groups
Author: Clarke, Robert John
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 1969
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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.
Supervisor: Not available Sponsor: Commonwealth Scholarship Commission (CSC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.594878  DOI: Not available
Keywords: QA Mathematics
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