Lie centrally metabelian group rings in characteristic 3
Let \(L\) be a Lie algebra over a field \(F\), \(L'=[L,L]\) and \(L''=(L')'\). The Lie algebra \(L\) is called centrally metabelian if \([L'',L]=0\). Let \(A\) be an associative unitary algebra over a field \(F\) and let \({\mathfrak L} (A)\) be the Lie algebra which has the same underlying vector space as \(A\) and which satisfies \([a,b]=ab-ba\) for \(a, b\in A\). The algebra \(A\) is called Lie centrally metabelian if \({\mathfrak L}(A)\) is centrally metabelian. Let \(FG\) be the group algebra of a group \(G\) over a field \(F\) of characteristic 3. A necessary and sufficient condition for \(FG\) to be centrally metabelian is given. It is the main result of the paper.
scientific article; zbMATH DE number 869803