Geodesic
On maximal subgroup of a finite solvable group
Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 129-134 
D. V. Gritsuk; V. S. Monakhov. On maximal subgroup of a finite solvable group. Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 129-134. http://geodesic.mathdoc.fr/item/EMJ_2012_3_2_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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

[1] K. Doerk, T. Hawkes, Finite soluble groups, de Gruyter, Berlin–New York, 1992 | MR | Zbl

[2] B. Huppert, Endliche Gruppen, v. I, Berlin–Heidelberg–New York, 1967 | Zbl

[3] V. A. Vedernikov, “On $\pi$-properties of a finite groups”, Arithmetic and subgroup structure of finite groups, Science and technics, Minsk, 1986, 13–19 (in Russian) | MR