Group algebras whose symmetric elements are Lie metabelian

Let F be a field of characteristic p not equal 2 and G a group without 2- elements having an involution *. Write (FG)^(+) for the set of elements in the group ring FG that are symmetric with respect to the induced involution. In the present note, we show that if G is finite and (FG)^(+) is Lie metabelian, then G is nilpotent. Based on this result, we deduce that if G is torsion, p not equal 3 and (FG)^(+) is Lie metabelian, then G must be abelian. This extends a result of Levin and Rosenberger.