In this paper, we investigate the p p -supersolvability of a finite group in which some p p -subgroups satisfy a subgroup embedding property and we extend some known results.

A subgroup H of a group G is called Φ-s-supplemented in G if there exists a subnormal subgroup K of G such that G = HK and H ∩ K ≤ Φ (H), where Φ (H) is the Frattini subgroup of H. We investigate the ...