The Library
Radicals of group algebras and permutation representations of symplectic groups
Tools
Tools
Tools
Clarke, Robert John (1969) Radicals of group algebras and permutation representations of symplectic groups. PhD thesis, University of Warwick.
|
PDF
WRAP_Thesis_Clarke_1969.pdf - Requires a PDF viewer. Download (2409Kb) | Preview |
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 (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: |
|
||||
| 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| Publication Status: | Unpublished | ||||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 |
Request changes or add full text files to a record
Repository staff actions (login required)
 |
View Item |
Downloads
Downloads per month over past year
