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dc.contributor Ph.D. Program in Mathematics.
dc.contributor.advisor Coşkun, Olcay.
dc.contributor.author Muslumov, Ruslan.
dc.date.accessioned 2023-10-15T11:16:11Z
dc.date.available 2023-10-15T11:16:11Z
dc.date.issued 2022
dc.identifier.other MATH 2022 M87 PhD
dc.identifier.uri http://digitalarchive.boun.edu.tr/handle/123456789/19904
dc.description.abstract 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 over finite groups, whose morphism sets are given by the kB(G,H) groups. A biset functor defined on kC, with values in k-Mod is a k-linear functor from kC to the category of k-Mod. The remarkable results as the evaluation of the Dade group of endopermutation modules of a p- group and finding the unit group of the Burnside ring of a p- group are done using the theory of biset functors. Looking for ring objects in the category of biset functors one gets a more sophisticated structure, which is called a Green Biset Functor. Serge Bouc introduced the slice Burnside ring and the section Burnside ring for a finite group G. He also showed that these two rings have a natural structure of a Green Biset Functor. In our work we classify simple modules over the section Burnside ring of G using the approach of the paper Fibered Biset Functors by Robert Boltje and Olcay Coşkun.
dc.publisher Thesis (Ph.D.) - Bogazici University. Institute for Graduate Studies in Science and Engineering, 2022.
dc.subject.lcsh Simplexes (Mathematics)
dc.title Simple section biset functors
dc.format.pages viii, 60 leaves


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