Bounded Engel and solvable unitary units in group rings

Abstract Let FG be the group ring of a group G over a field F . We consider the group of unitary units of FG with respect to the classical involution. Under suitable restrictions upon F , we show that if the unitary units of FG are both bounded Engel and solvable, then the entire unit group of FG is nilpotent. This extends a result of Fisher, Parmenter and Sehgal.