On Shemetkov's theorem about the complementedness of the residual

A formation $\mathfrak F$ of finite groups is called a $GWP$-formation if the $\mathfrak F$-residual of the group generated by two $\mathfrak F$-subnormal subgroups is the subgroup generated by their $\mathfrak F$-residuals. The main aim of the article is to find some sufficient conditions for a finite group to split over its $\mathfrak F$-residual.