Group algebras with centrally metabelian unit groups
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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.
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Sahai, M. “Group algebras with centrally metabelian unit groups”. Publicacions Matemàtiques, vol.VOL 40, no. 2, pp. 443-56, https://raco.cat/index.php/PublicacionsMatematiques/article/view/37876.
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