dc.contributor.advisor Barker, Laurence John en_US dc.contributor.author Mutlu, Hatice en_US dc.date.accessioned 2019-07-08T10:58:06Z dc.date.available 2019-07-08T10:58:06Z dc.date.copyright 2019-06 dc.date.issued 2019-06 dc.date.submitted 2019-06-04 dc.identifier.uri http://hdl.handle.net/11693/52147 dc.description Cataloged from PDF version of article. en_US dc.description Thesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2019. en_US dc.description Includes bibliographical references (leaves (101-102). en_US dc.description.abstract Green functors are a kind of group functor, rather like Mackey functors, but en_US 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. dc.description.statementofresponsibility by Hatice Mutlu en_US dc.format.extent vii, 102 leaves ; 30 cm. en_US dc.language.iso English en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.subject Green functors en_US dc.subject P-permutation modules en_US dc.subject Canonical induction formula en_US dc.subject Burnside ring en_US dc.subject Monomial Burnside ring en_US dc.subject Tensor induction en_US dc.subject Lefschetz invariant en_US dc.title Canonical induction, Green functors, lefschetz invariant of monomial G-posets en_US dc.title.alternative Kuralsal indüksiyon, Green izleçleri, tek terimli G-kısmi sıralı kümelerinin lefschetz değişmezleri en_US dc.type Thesis en_US dc.department Department of Mathematics en_US dc.publisher Bilkent University en_US dc.description.degree Ph.D. en_US dc.identifier.itemid B153317 dc.embargo.release 2020-01-04
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