The Hall property $\mathcal{D}_π$ is inherited by overgroups of $π$-Hall subgroups

Let $π$ be a set of primes. We say that a finite group $G$ is a $\mathcal{D}_π$-group if the maximal $π$-subgroups of $G$ are conjugate. In this paper, we give an affirmative answer to Problem 17.44(b) from "Kourovka notebook", namely we prove that in a $\mathcal{D}_π$-group an overgroup of a $π$-Hall subgroup is always a $\mathcal{D}_π$-group.

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