On the heritability of the Hall property $D_\pi$ by overgroups of $\pi$-Hall subgroups

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Abstract

Let $\pi$ be a set of primes. We say that a finite group $G$ is a $D_\pi$-group if all its maximal $\pi$-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 $D_\pi$-group an overgroup of a $\pi$-Hall subgroup is always a $D_\pi$-group.