Fitting classes with given properties of Hall subgroups

In the theory of formations of finite solvable groups, there is a well-known result due to Blessenohl claiming that, for any local formation F, the class of groups for which every Hall π -subgroup belongs to F also is a local formation. In the present paper, we obtain a result exactly dual to that indicated in the theory of Fitting classes. We prove that if a Fitting class F is local, then the class of all groups all of whose Hall π -subgroups belong to F is also local