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 |
|