Geodesic
Heritability of the property $\mathcal D_\pi$ by overgroups of $\pi$-Hall subgroups in the case where $2\in\pi$
Algebra i logika, Tome 53 (2014) no. 1, pp. 26-44

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Let $\pi$ be a set of prime numbers. We say that a finite group $G$ is a $\mathcal D_\pi$-group if all of its maximal $\pi$-subgroups are conjugate. Question 17.44(b) in Unsolved Problems in Group Theory, The Kourovka Notebook, asks whether an overgroup of a $\pi$-Hall subgroup of a $\mathcal D_\pi$-group is always a $\mathcal D_\pi$-group. We give an affirmative answer to this question in the case where $2\in\pi$.
Keywords: finite group, $\pi$-Hall subgroup, $\mathcal D_\pi$-group, group of Lie type, finite simple group, maximal subgroup of odd index. 
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     author = {N. Ch. Manzaeva},
     title = {Heritability of the property $\mathcal D_\pi$ by overgroups of $\pi${-Hall} subgroups in the case where~$2\in\pi$},
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     pages = {26--44},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/AL_2014_53_1_a2/}
}
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N. Ch. Manzaeva. Heritability of the property $\mathcal D_\pi$ by overgroups of $\pi$-Hall subgroups in the case where $2\in\pi$. Algebra i logika, Tome 53 (2014) no. 1, pp. 26-44. http://geodesic.mathdoc.fr/item/AL_2014_53_1_a2/