On the (crossed) Burnside ring of profinite groups

TL;DR

This paper explores properties of the Burnside ring for profinite groups, introduces the crossed Burnside ring for profinite FC-groups, and generalizes finite group results to profinite settings.

Contribution

It introduces the crossed Burnside ring for profinite FC-groups and extends finite group results to the profinite context.

Findings

Properties of the Burnside ring for profinite groups analyzed

Introduction of the crossed Burnside ring for profinite FC-groups

Generalization of finite group results to profinite groups

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.