Cohomology of infinite groups realizing fusion systems

buir.advisorYalçın, Ergün
dc.contributor.authorGündoğan, Muhammed Said
dc.date.accessioned2019-09-17T12:30:43Z
dc.date.available2019-09-17T12:30:43Z
dc.date.copyright2019-09
dc.date.issued2019-09
dc.date.submitted2019-09-12
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2019.en_US
dc.descriptionIncludes bibliographical references (leaves 66-68).en_US
dc.description.abstractGiven a fusion system F defined on a p-group S, there exist infinite group 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.en_US
dc.description.provenanceSubmitted by Betül Özen (ozen@bilkent.edu.tr) on 2019-09-17T12:30:43Z No. of bitstreams: 1 thesis.pdf: 459026 bytes, checksum: 1a678a6ac947e58988bd5b279fd387ec (MD5)en
dc.description.provenanceMade available in DSpace on 2019-09-17T12:30:43Z (GMT). No. of bitstreams: 1 thesis.pdf: 459026 bytes, checksum: 1a678a6ac947e58988bd5b279fd387ec (MD5) Previous issue date: 2019-09en
dc.description.statementofresponsibilityby Muhammed Said Gündoğanen_US
dc.format.extentviii, 68 leaves ; 30 cm.en_US
dc.identifier.itemidB105338
dc.identifier.urihttp://hdl.handle.net/11693/52444
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectFusion systemsen_US
dc.subjectCohomology of groupsen_US
dc.subjectCohomology of fusion systemsen_US
dc.subjectGraph of groupsen_US
dc.titleCohomology of infinite groups realizing fusion systemsen_US
dc.title.alternativeFüzyon sistemlerini gerçekleyen sonsuz grupların kohomolojisien_US
dc.typeThesisen_US
thesis.degree.disciplineMathematics
thesis.degree.grantorBilkent University
thesis.degree.levelDoctoral
thesis.degree.namePh.D. (Doctor of Philosophy)

Files

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
thesis.pdf
Size:
448.27 KB
Format:
Adobe Portable Document Format
Description:
Full printable version

License bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description: