On $S$-Quasinormally Embedded Subgroups of Finite Groups

A subgroup $H$ of a group $G$ is said to be $S$-quasinormally embedded in $G$ if for every Sylow subgroup $P$ of $H$, there is an $S$-quasinormal subgroup $K$ in $G$ such that $P$ is also a Sylow subgroup of $K$. Groups with certain $S$-quasinormally embedded subgroups of prime power order are studied. We prove Theorems 1.4, 1.5 and 1.6 of [10] remain valid if we omit the assumption that $G$ is a group of odd order.