First Cohomology of Some Infinitely Generated Groups

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dc.contributor.authorEastridge, Samuel Vanceen
dc.contributor.committeechairLinnell, Peter A.en
dc.contributor.committeememberMihalcea, Constantin Leonardoen
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberRossi, John F.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2017-04-25T22:29:01Zen
dc.date.available2017-04-25T22:29:01Zen
dc.date.issued2017-04-25en
dc.description.abstractThe goal of this paper is to explore the first cohomology group of groups G that are not necessarily finitely generated. Our focus is on l^p-cohomology, 1 leq p leq infty, and what results regarding finitely generated groups change when G is infinitely generated. In particular, for abelian groups and locally finite groups, the l^p-cohomology is non-zero when G is countable, but vanishes when G has sufficient cardinality. We then show that the l^infty-cohomology remains unchanged for many classes of groups, before looking at several results regarding the injectivity of induced maps from embeddings of G-modules. We present several new results for countable groups, and discuss which results fail to hold in the general uncountable case. Lastly, we present results regarding reduced cohomology, including a useful lemma extending vanishing results for finitely generated groups to the infinitely generated case.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:10011en
dc.identifier.urihttp://hdl.handle.net/10919/77517en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectGroup Cohomologyen
dc.subjectUncountableen
dc.subjectLocally Finiteen
dc.titleFirst Cohomology of Some Infinitely Generated Groupsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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