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