We study D_ -groups with a trivial solvable radical that do not have nontrivial normal -subgroups in which all simple nonabelian factors of their subnormal series are simple sporadic groups. It is proved that in such groups, for any -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.
Belousov et al. (Fri,) studied this question.