On some product of $\mathrm{SM}$-groups

A subgroup $A$ of a group $G$ is called $\mathrm{tcc}$-subgroup in $G$, if there is a subgroup $T$ of $G$ such that $G=AT$ and for any $X\le A$ and $Y\le T$ there exists an element $u\in \langle X,Y\rangle $ such that $XY^u\leq G$. The notation $H\le G $ means that $H$ is a subgroup of a group $G$. In this paper we proved that the class of all $\mathrm{SM}$-groups is closed under the product of $\mathrm{tcc}$-subgroups. Here an $\mathrm{SM}$-group is a group where each subnormal subgroup permutes with every maximal subgroup.