Let \(G\) be a finite group and \(H\le G\) . \(H\) is said to be NSP in \(G\) if for every prime \(q\not \mid |H|\) and for every \(K\le G\) with \(H\le K\) , there exists \(Q\in \,\) Syl \(_q(K)\) such that \(Q\le N_{K}(H)\) . Moreover, \(H\) is said to be weakly NSP in \(G\) if there exists \(T \unlhd G\) such that \(G = HT\) and \(H \cap T\) is nearly \(S\) -permutable in \(G\) . In this paper, by assuming that some primary subgroups of \(G\) are either weakly NSP in \(G\) or have \(p\) -nilpotent supplements in \(G\) , the \(p\) -nilpotency and supersolvability of \(G\) is given.
