Finite groups with some weakly SΦ-supplemented subgroups

Let G be a finite group. A subgroup H of G is called s-permutable in G if H permutes with every Sylow subgroup of G. A subgroup H of G is called weakly S Phi-supplemented in G if there exists a subgroup K of G such that G = HK and H boolean AND K <= Phi(H)H-sG, where Phi(H) is the Frattini subgroup of H and H-sG is the subgroup of H generated by all these subgroups of H that are s-permutable in G. Using this concept, some results for a group to be p-nilpotent and supersolvable are given. These results improve and extend some new and recent results in the literature.