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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
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 or Dissertation (PhD) | ||||
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| 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: |
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| 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| Publication Status: | Unpublished | ||||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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