Finite groups in which SS-permutability is a transitive relation

A subgroup $H$ of a finite group $G$ is said to be SS-permutable in $G$ if $H$ has a supplement $K$ in $G$ such that $H$ permutes with every Sylow subgroup of $K$. A finite group $G$ is called an SST-group if SS-permutability is a transitive relation on the set of all subgroups of $G$. The structure of SST-groups is investigated in this paper.