The group extensions problem and its resolution in cohomology for the case of an elementary abelian normal sub-group
Date
2018
Authors
Adams, Zachary W., author
Hulpke, Alexander, advisor
Patel, Amit, committee member
Bohm, Wim, committee member
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Abstract
The Jordan-Hölder theorem gives a way to deconstruct a group into smaller groups, The converse problem is the construction of group extensions, that is to construct a group G from two groups Q and K where K ≤ G and G/K ≅ Q. Extension theory allows us to construct groups from smaller order groups. The extension problem then is to construct all extensions G, up to suitable equivalence, for given groups K and Q. This talk will explore the extension problem by first constructing extensions as cartesian products and examining the connections to group cohomology.
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Subject
group extension
group cohomology
group theory