On maximal subgroup of a finite solvable group

Abstract

Let \(H\) be a non-normal maximal subgroup of a finite solvable group \(G\), and let \(q \in \pi(F(H / \mathrm{Core}_G H))\). It is proved that \(G\) has a Sylow \(q\)-subgroup \(Q\) such that \(N_G(Q) \subseteq H\).