Group algebras with centrally metabelian unit groups

Resum

Given a field $K$ of characteristic $p > 2$ and a finite group $G$, necessary and sufficient conditions for the unit group $U(KG)$ of the group algebra $KG$ to be centrally metabelian are obtained. It is observed that $U(KG)$ is centrally metabelian if and only if $KG$ is Lie centrally metabelian.