Group algebras whose symmetric and skew elements are Lie solvable

Let FG be the group algebra of a group G without 2-elements over a field F of characteristic p ≠ 2 endowed with the canonical involution induced from the map g g-1, g ∈ G. Let (FG)- and (FG)+ be the sets of skew and symmetric elements of FG, respectively, and let P denote the set of p-elements of G (with P = 1 if p = 0). In the present paper we prove that if either P is finite or G is non-torsion and (FG)- or (FG)+ is Lie solvable, then FG is Lie solvable. The remaining cases are also settled upon small restrictions. © de Gruyter 2009.