On -z-supplemented subgroups of finite groups

A subgroup H of a group G is called -z-supplemented in G if there exists a subgroup K of G, such that G = H K and H ∩ K ≤ Z∞(G), where Z∞(G) is the -hypercenter of G. We obtain some results about the -z-supplemented subgroups and use them to determine the structure of some groups.