h-conditionally permutable subgroups and PST-groups

‎A subgroup $H$ of a finite group $G$ is said to be $h$-conditionally permutable in $G$ if for every Hall subgroup $X$ of $G$‎, ‎there exists an element $g\in G$ such that $HX^{g}=X^{g}H$‎. ‎In this paper‎, ‎we obtain some results on $h$-conditionally permutable and by using this results‎, ‎we are able to determine some new characterizations of solvable PST-groups