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dc.contributor.authorEastridge, Samuel Vanceen_US
dc.date.accessioned2017-04-25T22:29:01Z
dc.date.available2017-04-25T22:29:01Z
dc.date.issued2017-04-25en_US
dc.identifier.othervt_gsexam:10011en_US
dc.identifier.urihttp://hdl.handle.net/10919/77517
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_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis item is protected by copyright and/or related rights. Some uses of this item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectGroup Cohomologyen_US
dc.subjectUncountableen_US
dc.subjectLocally Finiteen_US
dc.titleFirst Cohomology of Some Infinitely Generated Groupsen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairLinnell, Peter A.en_US
dc.contributor.committeememberMihalcea, Constantin Leonardoen_US
dc.contributor.committeememberBall, Joseph A.en_US
dc.contributor.committeememberRossi, John F.en_US


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