The existence of pronormal $π$-Hall subgroups in $E_π$-groups

A subgroup $H$ of a group $G$ is called {\it pronormal}, if for every $g\in G$ subgroups $H$ and $H^g$ are conjugate in $\langle H, H^g\rangle$. It is proven that if a finite group $G$ possesses a $π$-Hall subgroup for a set of primes $π$, the every its normal subgroup (in particular, $G$ itself) possesses a $π$-Hall subgroup that is pronormal in~$G$.

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