Geodesic
Towards Huppert--Shemetkov's theorem
Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 64-66.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/

[1] Shemetkov L.A., “O konechnykh razreshimykh gruppakh”, Izv. AN SSSR. Ser. matematika, 32:3 (1968), 533–559 | MR | Zbl

[2] Huppert B., “Normalteiler und maximale Untergruppen endlicher Gruppen”, Math. Z., 60 (1954), 409–434 | DOI | MR | Zbl

[3] Huppert B., Endliche Gruppen I, Berlin, Heidelberg, New York, 1967, 793 pp. | MR | Zbl

[4] Pazderski G., “Über lineare auflosbare Gruppen”, Math. Nachr., 45 (1970), 1–68 | DOI | MR | Zbl

[5] Gashutz W., “Existenz und Konjugiertsein von Untergruppen, die in endlichen auflosbaren Gruppen durch gewisse Indexschranken definiert sind”, J. Algebra, 53:2 (1978), 389–394 | DOI | MR