Abstract:
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.
Citation:
V. N. Zagurskii, N. T. Vorob'ev, “Fitting Classes with Given Properties of Hall Subgroups”, Mat. Zametki, 78:2 (2005), 234–240; Math. Notes, 78:2 (2005), 213–218