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