The Athens Algebra Seminar presents Darren Simmons discussing “Group Cohomology and the Extension Problem” on Thursday, Dec. 3, from 4:35-5:30 p.m. on Morton 218.
Abstract: An extension of a group G by a group N is a short exact sequence of groups of the form
{e} → N → E → G → {e}
The group E is, by abuse of language, also called an extension of G by N. In such an exact sequence, N is normal in E, and E/N is isomorphic to G. A classical problem of algebra—the extension problem—is classifying such sequences, given G and N, which amounts to finding groups E fitting in the diagram. In this talk, we will introduce the technique of group cohomology, which can be used in solving the extension problem. We will also demonstrate how group cohomology can be used to solve the extension problem. This talk is targeted towards graduate students; some familiarity with semidirect products of groups will be assumed.
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