LIE NILPOTENCY OF GROUP-RINGS

Let FG be the group algebra of a group G over a field F. Denote by t he natural involution, (SIGMA f(i)g(i)) = SIGMAf(i) . g(i)-1. Let S a nd K denote the set of symmetric and skew symmetric elements respectiv ely with respect to this involution. It is proved that if the characte ristic of F is zero or p not-equal 2 and G has no 2-elements, then the Lie nilpotence of S or K implies the Lie nilpotence of FG.