On S*--Supplemented Subgroups of Finite Groups (1) (P--Nilpotent Groups, Primary Subgroups, Supplemented Subgroups, Solvable Group‪)‬

Abstract A subgroup H of a group G is said to be [s.sup.*]--supplemented subgroups in G if there exists a subgroup K of G such that G = HK and H [intersection] K [less than or equal to] [H.sub.SG], where [H.sub.SG] is the largest subnormal subgroup of G contained in H. In this paper we determine the structure of finite groups with [s.sup.*]--supplemented primary subgroups,and obtain some new results about p--nilpotent groups. Keywords P--nilpotent groups, primary subgroups, [s.sup.*]--supplemented subgroups, solvable group.