On Lie metabelian group rings
For a commutative ring \(R\) in which \(2 \neq 0\) and a finite group \(G\) of order prime to 6 it is shown that each of the properties below implies \(G\) to be abelian. (i) The subring of the group ring \(RG\) which is generated by all \(g + g^{-1}\), \(g \in G\) is Lie metabelian. (ii) The subring generated by all \(g - g^{-1}\) is Lie metabelian.
scientific article; zbMATH DE number 687811