On Minimal Weakly NS*-Supplemented Subgroups of Finite Groups

Let G be a finite group. A subgroup H of G is called nearly S-permutable in G if for every prime p with (p, |H|) = 1 and for every subgroup K of G containing H the normalizer NK(H) contains some Sylow p-subgroup of K. A subgroup H of G is said to be weakly NS*-supplemented subroup of G if there exists a subgroup T of G such that G = HT, and H boolean AND T <= HnG, where HnG is the subgroup of H generated by all those subgroups of H which are nearly S-permutable in G. In this article, we investigate the structure of G under the assumption that every subgroups of prime order are weakly NS*-permutable subgroups of G. Some recent results are generalized.