On Subgroups Generated by Small Classes in Finite Groups

Let G be a finite group and M(G) be the subgroup of G generated by all noncentral elements of G that lie in the conjugacy classes of the smallest size. Recently several results have been proved regarding the nilpotency class of M(G) and F(M(G)), where F(M(G)) denotes the Fitting subgroup of M(G). We prove some conditional results regarding the nilpotency class of M(G).