Geodesic
On maximal subgroup of a~finite solvable group
Eurasian mathematical journal, Tome 3 (2012) no. 2, pp. 129-134

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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 $N_G(Q)\subseteq H$. 
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     author = {D. V. Gritsuk and V. S. Monakhov},
     title = {On maximal subgroup of a~finite solvable group},
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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/