One characterization of the Gaschütz subgroup of a finite soluble group

Let $H$ be an $\mathfrak{N}$-prefrattini subgroup of a soluble finite group $G$ and $\Delta(G)$ be its Gaschütz subgroup. In this paper, it is proved that there exist elements $x,y \in G$ such that the equality $H \cap H^x \cap H^y = \Delta (G)$ holds.