On maximal subgroup of a finite solvable group - Gritsuk, Dmitry Vladimirovich; Monakhov, Victor Stepanovich (Eurasian Mathematical Journal, 2012)
Let \(H\) be a non-normal maximal subgroup of a finite solvable group \(G\), and let \(q π(F(H / Core_G H))\). It is proved that \(G\) has a Sylow \(q\)-subgroup \(Q\) such that \(N_G(Q) H\).