Geodesic
On the heritability of the Sylow $\pi$-theorem by subgroups
Sbornik. Mathematics, Tome 211 (2020) no. 3, pp. 309-335

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Let $\pi$ be a set of primes. We say that the Sylow $\pi$-theorem holds for a finite group $G$, or $G$ is a $\mathscr D_\pi$-group, if the maximal $\pi$-subgroups of $G$ are conjugate. Obviously, the Sylow $\pi$-theorem implies the existence of $\pi$-Hall subgroups. In this paper, we give an affirmative answer to Problem 17.44, (b), in the Kourovka notebook: namely, we prove that in a $\mathscr D_\pi$-group an overgroup of a $\pi$-Hall subgroup is always a $\mathscr D_\pi$-group. Bibliography: 52 titles.
Keywords: finite group, $\pi$-Hall subgroup, group of Lie type, maximal subgroup.
Mots-clés : $\mathscr D_\pi$-group 
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     title = {On the heritability of the {Sylow} $\pi$-theorem by subgroups},
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E. P. Vdovin; N. Ch. Manzaeva; D. O. Revin. On the heritability of the Sylow $\pi$-theorem by subgroups. Sbornik. Mathematics, Tome 211 (2020) no. 3, pp. 309-335. http://geodesic.mathdoc.fr/item/SM_2020_211_3_a0/