Weakly C*-Normal Subgroups and p-Nilpotency of Finite Groups

A subgroup H is called to be weakly c*-normal in G if there exists a subnormal subgroup K such that G = HK and H∩ K is s-quasi normal embedded in G.The following result is established: Let G be a group such that G is S4-free. Also let p be the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If every minimal subgroup of P of order p or 4 (when p = 2) is weakly c*-normal in NG(P) and when p = 2 P is quaternion-free, then G is p-nilpotent.The main result is established and a generalization of some authors’.