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

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      Author(s)
      Karagüzel, Çisil
      Advisor
      Barker, Laurence J.
      Date
      2016-07
      Publisher
      Bilkent University
      Language
      English
      Type
      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.
      Keywords
      Biset functors
      P-permutation modules
      Simple composition factors
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      http://hdl.handle.net/11693/32153
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      • Dept. of Mathematics - Master's degree 125
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