On the Wielandt subgroup of generalized FC-groups

We extend to soluble FC*-groups, the class of generalized FC-groups introduced in [de Giovanni, Russo and Vincenzi, Groups with restricted conjugacy classes, Serdica Math. J. 28(3) (2002) 241–254], the characterization of finite soluble T-groups, and some results on the Wielandt subgroup, obtained recently in [Kaplan, On finite T-groups and the Wielandt subgroup, J. Group Theory. 14 (2011) 855–863].