On intersections of $\pi$-Hall subgroups of some $D_\pi$-groups

We study $D_\pi$-groups with a unit solvable radical that do not have nontrivial normal $\pi$-subgroups in which all simple nonabelian factors of their subnormal series are simple sporadic groups. It is proved that in such groups, for any $\pi$-Hall subgroup $H$, there exists an element $g$ such that $H\cap H^g=1$. Thus, Question 20.123 (c) of the Kourovka Notebook is solved and, under the above conditions, a positive answer is given to Question 18.31.