On Intersections of π-Hall Subgroups of Some D_π-Groups

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