dc.contributor.advisor Yalçın, Ergün dc.contributor.author Gündoğan, Muhammed Said dc.date.accessioned 2019-09-17T12:30:43Z dc.date.available 2019-09-17T12:30:43Z dc.date.copyright 2019-09 dc.date.issued 2019-09 dc.date.submitted 2019-09-12 dc.identifier.uri http://hdl.handle.net/11693/52444 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 66-68). en_US dc.description.abstract Given a fusion system F defined on a p-group S, there exist infinite group en_US models, constructed by Leary and Stancu, and Robinson, that realize F. We study these models when F is a fusion system of a finite group G. If the fusion system is given by a finite group, then it is known that the cohomology of the fusion system and the Fp-cohomology of the group are the same. However, this is not true in general when the group is infinite. For the fusion system F given by finite group G, the first main result gives a formula for the difference between the cohomology of an infinite group model realizing the fusion F and the cohomology of the fusion system. The second main result gives an infinite family of examples for which the cohomology of the infinite group obtained by using the Robinson model is different from the cohomology of the fusion system. The third main result gives a new method for the realizing fusion system of a finite group acting on a graph. We apply this method to the case where the group has p-rank 2, in which case the cohomology ring of the fusion system is isomorphic to the cohomology of the group. dc.description.statementofresponsibility by Muhammed Said Gündoğan en_US dc.format.extent viii, 68 leaves ; 30 cm. en_US dc.language.iso English en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.subject Fusion systems en_US dc.subject Cohomology of groups en_US dc.subject Cohomology of fusion systems en_US dc.subject Graph of groups en_US dc.title Cohomology of infinite groups realizing fusion systems en_US dc.title.alternative Füzyon sistemlerini gerçekleyen sonsuz grupların kohomolojisi 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 B105338
﻿