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

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.