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Group Cohomology and Extensions

dc.contributor.advisorPrasolov, Andrei
dc.contributor.authorBreivik, Markus Nordvoll
dc.date.accessioned2019-09-23T07:50:37Z
dc.date.available2019-09-23T07:50:37Z
dc.date.issued2019-08-31
dc.description.abstractThe goal of this thesis is to classify all extensions where the kernel has order p^s and the cokernel has order p^t, p is a prime, and 1 ≤ s,t ≤ 2. We determine (up to weak congruence) the different combinations of kernel, cokernel and operators, and for each case, calculate the second cohomology group. By comparing resolutions, we get an explicit correspondence between the second cohomology group and the group of congruence classes of extensions. Using this construction, we determine (up to congruence) the extensions for the different combinations.en_US
dc.identifier.urihttps://hdl.handle.net/10037/16251
dc.language.isoengen_US
dc.publisherUiT Norges arktiske universiteten_US
dc.publisherUiT The Arctic University of Norwayen_US
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2019 The Author(s)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-sa/4.0en_US
dc.rightsAttribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)en_US
dc.subject.courseIDMAT-3900
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410::Algebra/algebraic analysis: 414en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Algebra/algebraisk analyse: 414en_US
dc.subjecthomological algebraen_US
dc.subjecthomologyen_US
dc.subjectcohomologyen_US
dc.subjectgroup cohomologyen_US
dc.subjectgroup extensionen_US
dc.subjectgroup extensionsen_US
dc.subjectintegral group ringen_US
dc.subjectshort exact sequenceen_US
dc.subjectexact sequenceen_US
dc.subjectresolutionen_US
dc.subjectmoduleen_US
dc.subjectmodulesen_US
dc.subjectp-groupsen_US
dc.subjectcocycleen_US
dc.subjectcocyclesen_US
dc.subjectcoboundaryen_US
dc.subjectcoboundariesen_US
dc.subjectresolutionsen_US
dc.subjectkernelen_US
dc.subjectcokernelen_US
dc.titleGroup Cohomology and Extensionsen_US
dc.typeMaster thesisen_US
dc.typeMastergradsoppgaveen_US


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