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Brauer relations, induction theorems and applications.
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Spencer, Matthew (2017) Brauer relations, induction theorems and applications. PhD thesis, University of Warwick.
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WRAP_Theses_Spencer_2017.pdf - Submitted Version - Requires a PDF viewer. Download (1279Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3110328~S15
Abstract
Let G be a finite group and F a field, then to any finite G-set X we may associate a F [G]-permutation module whose F -basis is indexed by elements of X. We seek to describe when two non-isomorphic G-sets give rise isomorphic permutation modules. This amounts to describing the kernel KF(G) of a map between the Burnside Ring of G and the ring of representation ring of F [G]-representations of G. Elements of this kernel are known as Brauer Relations and have extensive applications in Number Theory, for example giving relationships between class numbers of the in-termediate Number fields of a Galois extension. In characteristic 0, the generators of KF(G) have been classified in [2]. We extend this classification to characteristic p > 0 for all finite groups G save for groups which admit a subquotient which is an extension of a non-elementary p-quasi-elementary group by a p-group. Our approach initially mimics that in characteristic 0, and so we give a much more general description of these steps in terms of Green functors.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Brauer groups, Number theory, Galois theory, Green functors | ||||
Official Date: | May 2017 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Bartel, Alex | ||||
Extent: | v, 78 leaves. | ||||
Language: | eng |
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