Abstract: Let G be a finite group. A subgroup H of G is called nearly S-permutable in G if for every prime p with gcd (公式 and for every subgroup K of G containing H the normalizer N_K(H) contains some Sylow p-subgroup of K. A subgroup H of G is said to be 公式permutable subgroup of G if there exists a normal subgroup T of G such that HTG, π(G/T)π(H) and H∩T is nearly S-permutable subgroup of G. This article investigates the structure of G under the assumption that subgroups of prime power order are NS^*-permutable subgroups of G. Some recent results are generalized.

Key words: NS^*-permutable subgroups, p-nilpotent subgroups, supersolvable groups