The Lie Engel property in group algebras

Let F be a field and G any group. Denote the group of units of the group algebra FG by U(FG). In this talk, the Lie Engel property of the group algebra FG is investigated. It is known that if G is a torsion group, then FG is a bounded Lie Engel ring if and only if U(FG) is a bounded Engel group. Here, in particular, we show that if G is locally finite, then FG is a Lie Engel ring if and only if U(FG) is an Engel group. Further, if the characteristic of F is zero and U(FG) is Engel-by-finite, then we show that G is abelian