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Adrian Becedas: The second cohomology group and group extensions

Time: Mon 2019-05-20 10.00 - 11.00

Respondent: Adrian Becedas (BSc student)

Supervisor: Alexander Berglund

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Abstract: In this B.Sc. thesis we will show that for a group G and a G-module A there is a bijection between the second cohomology group H^2(G;A) and the equivalence classes of extensions pi0(Ext(G,A). This will be done by showing that there is an equivalence of categories from the category of 2-cocycles Z2(G;A) to the category of extensions Ext(G,A).

We will also, by examples, illustrate and show some computational use of some of the theory developed in the proof.