Browsing by Subject "Biset functors"

Now showing 1 - 4 of 4

Open Access
Biset functors and brauer's induction theorem
(2014) Öğüt, İsmail Alperen
We introduce two algebras on the endomorphism ring of the direct sum of character rings of groups from some collection. We prove the equality of these algebras to simplify a step in the proof of Brauer’s Induction Theorem. We also show that these algebras are isomorphic to the direct sum of character rings of the direct products of the groups from the collection.
Open Access
Equivariant Moore spaces and the Dade group
(Elsevier, 2017) Yalçın, E.
Let G be a finite p-group and k be a field of characteristic p. A topological space X is called an n-Moore space if its reduced homology is nonzero only in dimension n. We call a G-CW-complex X an n_-Moore G-space over k if for every subgroup H of G, the fixed point set XH is an n_(H)-Moore space with coefficients in k, where n_(H) is a function of H. We show that if X is a finite n_-Moore G-space, then the reduced homology module of X is an endo-permutation kG-module generated by relative syzygies. A kG-module M is an endo-permutation module if Endk(M)=M⊗kM⁎ is a permutation kG-module. We consider the Grothendieck group of finite Moore G-spaces M(G), with addition given by the join operation, and relate this group to the Dade group generated by relative syzygies. © 2017 Elsevier Inc.
Open Access
Obstructions for gluing biset functors
(Elsevier, 2019) Coşkun, O.; Yalçın, Ergün
We develop an obstruction theory for the existence and uniqueness of a solution to the gluing problem for a biset functor defined on the subquotients of a finite group G. The obstruction groups for this theory are the reduced cohomology groups of a category D∗ G whose objects are the sections (U, V ) of G, where 1 = V U ≤ G, and whose morphisms are defined as a generalization of morphisms in the orbit category. Using this obstruction theory, we calculate the obstruction group for some well-known p-biset functors, such as the Dade group functor defined on p-groups with p odd.
Open Access
On some of the simple composition factors of the biset functor of P-permutation modules
(2016-07) Karagüzel, Çisil
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.