Intersections of prefrattini subgroups in finite soluble groups

Abstract

‎Let $H$ be a prefrattini subgroup of a soluble finite group $G$‎. ‎In the‎ ‎paper it is proved that there exist elements $x,y in G$ such that the equality‎ ‎$H cap H^x cap H^y = Phi (G)$ holds‎.