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Title: Brauer relations, induction theorems and applications
Author: Spencer, Matthew
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2017
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics