SATURATED FORMATIONS CLOSED UNDER SYLOW NORMALIZERS

In this article we show that a finite soluble group possesses nilpotent Hall subgroups for well-defined sets of primes if and only if its Sylow normalizers satisfy the same property. In fact, this property of groups provides a characterization of the subgroup-closed saturated formations, whose elements are characterized by the Sylow normalizers belonging to the class, in the universe of all finite soluble groups.