On the $\mathrm{w}$-supersolubility of a finite group factorized by mutually permutable subgroups

The subgroups $A$ and $B$ of a group $G$ are called mutually permutable if $A$ permutes with all subgroups of $B$ and $B$ permutes with all subgroups of $A$. The sufficient conditions of $\mathrm{w}$-supersolubility of a group $G = AB$ that is factorized by two mutually permutable $\mathrm{w}$-supersoluble subgroups $A$ and $B$ were obtained. Besides we found the construction of $\mathrm{w}$-supersoluble residual of such group.