Finite groups with biprimary Hall subgroups

Let G be a finite group and let r be a prime divisor of the order of G  . We prove that if r≥5r≥5 and G   has the E{r,t}E{r,t}-property for all t∈π(G)\{r}t∈π(G)\{r}, then G is r-solvable. A group G   is said to have the EπEπ-property if G possesses a Hall π-subgroup.