The bounded Lie Engel property on torsion group algebras

Let F be a field of characteristic different from 2 and G a group with involution ∗. Extend the involution to the group ring FG, and write (FG)− for the Lie subalgebra of FG consisting of the skew elements. We classify the torsion groups G having no elements of order 2 such that (FG)− is bounded Lie Engel.