On Maximal Subgroups of a Finite Solvable Group

Abstract

The following result is received: Let $H$ be a non-normal maximal subgroup of a finite solvable group $G$ and let $q\in \pi (F(H/{\mathrm{Core}}_{G}H))$, then $G$ has a Sylow $q$-subgroup $Q$ such that $N_G(Q)\subseteq H$.