### On the (crossed) Burnside ring of profinite groups

Algebra Seminar

12th October 2022, 2:30 pm – 3:30 pm

Fry Building, 2.04

Given a finite group G, the Burnside ring B(G) of G is a commutative ring whose elements are virtual finite G-sets, i.e. finite sets endowed with an action of G. The crossed Burnside ring of G can be seen as a finite ring extension of B(G). In the late 80s, Dress and Siebeneicher introduced the Burnside rings of profinite groups and related their construction to that of Witt vectors. In this talk, we'll elaborate on their results, and introduce the crossed Burnside rings for a suitable class of profinite groups. We'll also present some elementary results about them.

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