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Browsing Matematik by Author "Coşkun, Olcay."

Browsing Matematik by Author "Coşkun, Olcay."

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  • A survey on endo - trivial modules 
    Sert, Gözde. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    In this thesis, we investigate endo-trivial modules and their classification endo trivial modules over p-groups. Endo-trivial modules were introduced by Dade [1] and appear naturally in moduler representation theory. Several ...
  • Complex representations of finite general linear groups 
    Küçük, Ebru Beyza. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    In this thesis, we determine complex irreducible representations of GL(2,K), the group of 2 by 2 invertible matrices over a finite field K. Actually, this is done by Ilya Piatetski-Shapiro in 1983. In his article [1], Shapiro ...
  • Composition factors of the functor of the complex characters 
    Arslan, Mehmet. (Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    When we consider CRC as a map sending any finite group G to the complex vector space CRC(G) of complex valued class functions on G, it becomes an A-fibered biset functor for any group A ≤ C×. Its structure is known for ...
  • Green biset functors and representation rings 
    Muslumov, Ruslan. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    In this thesis, we investigate Green biset functors and clasi cation of sipmle modules over a Green biset functors in some special cases. Our aim is to see what conditions on the Green functor makes simple modules over it ...
  • Modular representations of GL (2,p) 
    Karakurt, Turan. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2018., 2018.)
    In this thesis, we investigate representations of GLp2,pqby using indecomposable projective modules for GLp2,pq. Actually, this is pure module theoretic approach in parallel with [1] since we do not refer any character ...
  • On simple modules over the section burnside functor 
    Balçık, Irmak. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2016., 2016.)
    Biset functors provides a uni ed approach to module theoretic operations on representations of nite groups. It is well-known that biset functors can be considered as modules over the Green biset functor of the Burnside ...
  • Projective characters of finite groups 
    Yılmaz, Said. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)
    The purpose of this thesis to analyze the basic facts about projective characters of finite groups and compare them to the facts about ordinary characters of finite groups. We start with review of basic facts about the ...
  • Quotients of Hom-functors 
    Bilgin, Zehra. (Thesis (M.S.)-Bogazici University. Institute for Graduate Studies in Science and Engineering, 2012., 2012.)
    Quotients of Hom-functors are functors of the form HomR(P;{u100000})=HomR(P;{u100000})J where P is a projective R-module and J is a certain ideal of the endomorphism ring of P. These functors were used by R. Dipper in the ...
  • Relative endo-trivial modules 
    Budak, Doğa Ulaş. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2021., 2021.)
    We first develop the necessary tools from the theory of G-algebras and endomorphism rings. Then the basic results of Green's theory of vertices and sources for kG-modules is given. Building on these, we retrace the steps ...
  • Self - adjoint extension theory of singular interactions 
    Türköz, Mustafa. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2017., 2017.)
    In this thesis, we study two-dimensional finite singular point interactions and three-dimensional finite singular interactions supported by curves on a compact Riemannian manifold. Our aim is to show that finite rank perturbations ...
  • Simple section biset functors 
    Muslumov, Ruslan. (Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022., 2022)
    Let G and H be finite groups and k be a commutative unitary ring. The Burnside group B(G,H) is the Grothendieck group of the category of finite (G,H)-bisets. The biset category kC of finite groups is the category defined ...
  • The fibered burnside ring of a fusion system 
    Seviniş, Mert. (Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2019., 2019.)
    J. S. Reeh, in his PhD thesis [1], described the Burnside ring and its free basis for the fusion-stable sets. In this thesis we will extend his results for fibered sets. Basically we will use the same technics J.S. Reeh ...
  • The fibered p-biset functor of the fibered burnside ring 
    Yılmaz, Deniz. (Thesis (M.S.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2015., 2015.)
    We nd the composition factors of the A- bered Burnside functor kBA of p- groups over a eld k of characteristic q with q 6= p. We show that if A is a cyclic p-group, then kBA is uniserial. Moreover, we also show that the ...

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