Browsing by Subject "P-permutation modules"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Open Access Canonical induction, Green functors, lefschetz invariant of monomial G-posets(Bilkent University, 2019-06) Mutlu, HaticeGreen functors are a kind of group functor, rather like Mackey functors, but with a further multiplicative structure. They are defined on a category whose objects are finite groups and whose morphisms are generated by maps such as induction, restriction, inflation, deflation. The aim of this thesis is general formulation for canonical induction, suitable for Green functors, optionally equipped with inflations. Let p be a prime number. In Section 3, we apply the Boltje’s theory of canonical induction [1] to p-permutation modules and give a restriction-preserving Z[1/p]- linear canonical induction formula from the inflations of projective modules. In Section 4, we give a general formulation of canonical induction theory for Green biset functors equipped with induction, restriction, inflation maps. Let G be a finite group and C be an abelian group. In Section 5, motivated in part by a search for connection with Peter Symonds’ proof [2] of the integrality of a canonical induction formula, we introduce a Lefschetz invariant for the Cmonomial Burnside ring. These invariants let us to construct generalize tensor induction functors associated to any C-monomial (G, H)-biset from the category of C-monomial G-posets to the category of C-monomial H-posets. We will show that these functors induce well-defined tensor induction maps from BC(G) to BC(H), which in turn gives a group homomorphism BC(G) × → BC(H) × between the unit groups of C-monomial Burnside rings.Item Open Access On some of the simple composition factors of the biset functor of P-permutation modules(Bilkent University, 2016-07) Karagüzel, ÇisilLet 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.