Finite groups with $g$-permutable normalizers of sylow subgroups

Let $A$ and $B$ be subgroups in a finite group $G$. Then $A$ is (hereditarily) $G$-permutable with $B$ if $AB^x = B^xA$ for some $x \in G$ (for some $x \in \langle A,B\rangle $). A subgroup $A$ in $G$ is (hereditarily) $G$-permutable in $G$ if $A$ is (hereditarily) $G$-permutable with all subgroups in $G$. The article deals with the structure of $G$ such that the normalizers of Sylow subgroups are (hereditarily) $G$-permutable.