a subgroup $h$ is said to be $s$-permutable in a group $g$, if $hp=ph$ holds for every sylow subgroup $p$ of $g$. if there exists a subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every sylow subgroup of $b$, then $h$ is said to be $ss$-quasinormal in $g$. in this paper, we say that $h$ is a weakly $ss$-quasinormal subgroup of $g$, if there is a normal subgroup ...
