Products of F<sup>*</sup>(<i>G</i>)-subnormal subgroups of finite groups
A subgroup H of a finite group G is called F*( G )-subnormal if H is subnormal in H F*( G ). We show that if a group G is a product of two F*( G )-subnormal quasinilpotent subgroups, then G is quasinilpotent. We also study groups G = AB, where A is a nilpotent F*( G )-subnormal subgroup and B is a F*( G )-subnormal supersoluble subgroup. Particularly, we show that such groups G are soluble.