On the (crossed) Burnside ring of profinite groups

Mazza, Nadia (2022) On the (crossed) Burnside ring of profinite groups. Journal of Algebra. ISSN 0021-8693 (In Press)

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Abstract

In this paper we investigate some properties of the Burnside ring of a profinite group as defined in \cite{ds}. We introduce the notion of the crossed Burnside ring of a profinite FC-group, and generalise some results from finite to profinite (FC-)groups. In our investigations, we also obtain results on profinite FC-groups which may be of independent interest.