Lie ideals in group rings
Let U be a Lie ideal of the associative ring R and suppose that U is Lie nilpotent of class \(n\geq 3\). Then it is shown that \(\gamma_ 3(U)R\) is a nilpotent ideal of index at most 2n-4. Next, if R is a Lie nilpotent algebra of characteristic \(p>0\), then the Lie commutators generate a nil ideal of bounded exponent. Finally, let \(R=K[G]\) be the group algebra of the group G over the field K of characteristic \(p\geq 0\) and assume that R is Lie nilpotent of class less than n. If \(p=0\) or \(p\geq n\), then G is abelian. On the other hand, if \(p<n\) then G is nilpotent of class bounded by a function of n and p.
scientific article; zbMATH DE number 4129005