The 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. / Ph. D.
Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/77517 |
Date | 25 April 2017 |
Creators | Eastridge, Samuel Vance |
Contributors | Mathematics, Linnell, Peter A., Mihalcea, Constantin Leonardo, Ball, Joseph A., Rossi, John F. |
Publisher | Virginia Tech |
Source Sets | Virginia Tech Theses and Dissertation |
Detected Language | English |
Type | Dissertation |
Format | ETD, application/pdf |
Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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