Finite groups with F-subnormal normalizers of Sylow subgroups

Abstract

Let π be a set of primes and F be a formation. In this article a properties of the class w∗ πF of all groups G, such that π(G) ⊆ π(F) and the normalizers of all Sylow p-subgroups of G are F-subnormal in G for every p ∈ π ∩ π(G) are investigated. It is established that w∗ πF is a formation. Some hereditary saturated formations F for which w∗ πF = F are founded.