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arXiv · 1504.03137

On the heritability of the Hall property $D_π$ by overgroups of $π$-Hall subgroups

N. Ch. Manzaeva
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Abstract

Let $π$ be a set of primes. We say that a finite group $G$ is a $D_π$-group if all its maximal $π$-subgroups are conjugate. In this paper, we give an affirmative answer to the problem 17.44(b) from "The Kourovka notebook": we prove that in a $D_π$-group an overgroup of a $π$-Hall subgroup is always a $D_π$-group.

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N. Ch. Manzaeva. 2015-04-13. On the heritability of the Hall property $D_π$ by overgroups of $π$-Hall subgroups. https://arxiv.org/abs/1504.03137

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