GROUP ALGEBRAS WITH ENGEL UNIT GROUPS

Let F be afield of characteristic p >= 0 and G any group. In this article, the Engel property of the group of units of the group algebra FG is investigated. We show that if G is locally finite, then u(FG) is an Engel group if and only if G is locally nilpotent and G' is a p-group. Suppose that the set of nilpotent elements of FG is finite, It is also shown that if G is torsion, then u(FG) is an Engel group if and only if G' is a finite p-group and FG is Lie Engel, if and only if (FG) is locally nilpotent. If G is nontorsion but FG is semiprime, we show that the Engel property of it u(FG) implies that the set of torsion elements of G forms an abelian normal subgroup of G.