On some of the simple composition factors of the biset functor of P-permutation modules

Date
2016-07
Advisor
Barker, Laurence J.
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Bilkent University
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Language
English
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Thesis
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Abstract

Let k be an algebraically closed field of characteristic p, which is a prime, and C denote the field of complex numbers. Given a finite group G, letting ppk(G) denote the Grothendieck group of p-permutation kG-modules, we consider the biset functor of p-permutation modules, Cppk, by tensoring with C. By a theorem of Serge Bouc, it is known that the simple biset functors S H,V are parametrized by pairs (H, V ) where H is a finite group, and V is a simple COut(H)-module. At present, the full classification of the simple biset functors apparent in Cppk is not known. In this thesis, we find new simple functors SH;V apparent in Cppk where H is a specific type of p-hypo-elementary B-group. The technique for this result makes use of Maxime Ducellier's notion of a p-permutation functor and his use of D-pairs to classify the simple factors of the p-permutation functor of p-permutation modules Cpppk p-perm.

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Biset functors, P-permutation modules, Simple composition factors
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Published Version (Please cite this version)