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Injective Hulls of Trivial Modules

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We can model representations of abstract groups as modules of the corresponding group algebra; for example, those of abelian groups are modules of polynomial rings in some number of variables. The homological properties of such modules are in part determined by the minimal injective module containing them, the injective hull. In this talk I shall aim to demystify these hulls with explicit examples in the case of abelian groups, soluble groups and nilpotent p-adic groups.

This talk is an extended version of the one I will give at YRM in Bristol.

This talk is part of the Junior Algebra and Number Theory seminar series.

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