Finite Matrix Groups; Cohomology and Stable Elements

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• Anja Meyer, University of Loughborough
• Wednesday 21 May 2025, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Adam Jones.

In their 1956 book Cartan and Eilenberg present results which tell us that the modular cohomology of a finite group G is equal to the set of stable elements in the modular cohomology of a Sylow p-subgroup of G. In this talk we will look at the groups SL_2(Z/p^n) for n>1 and p any odd prime. Their cohomology is not yet known, however there is a way to obtain the cohomology, using a combination of tools from homological algebra, profinite group theory, and fusion systems. We will introduce the concepts used and show how they can facilitate the explicit computations, with p=3 as worked example.

This talk is part of the Algebra and Representation Theory Seminar series.

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