Geodesic
Towards Huppert–Shemetkov's theorem
Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 64-66 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that in every finite non-identity soluble group $G$ there exists a maximal subgroup $H$ such that $H$ does not contain the Fitting subgroup and $|G:H|=p^{r(G/\Phi(G))}$ for some prime number $p$. Here $r(G/\Phi(G))$ is the chief rank of the quotient $G/\Phi(G)$. 
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V. S. Monakhov. Towards Huppert–Shemetkov's theorem. Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 64-66. http://geodesic.mathdoc.fr/item/TIMB_2008_16_1_a10/

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