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Title: Homological methods in algebra
Author: Ford, Samuel
ISNI:       0000 0004 9352 7601
Awarding Body: University of York
Current Institution: University of York
Date of Award: 2019
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In this thesis, we apply homological methods to the study of groups in two ways: firstly, we generalise the results of [12] to a more general class of categories than posets, including finite groups which satisfy a particular cohomological condition. We then show that the only finite group satisfying this condition is the trivial group, but our results still hold in more generality than the originals, and we suggest a path to further generalisation. Secondly, we study the representation theory of certain groups by passing their actions on certain simplicial complexes to actions on the homologies of those complexes.
Supervisor: Everitt, Brent ; Bate, Michael Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available