On local properties of the formations of groups with $\mathrm{K}$-$\mathfrak{F}$-subnormal Sylow subgroups

The class of all finite groups with Sylow $\mathrm{K}$-$\mathfrak{F}$-subnormal subgroups is considered. The condition of saturation of this class is investigated, as well as the local screen in solvable case is established.