Injectors in fitting sets of finite groups

Abstract

A set of subgroups ℱ of a finite group G is referred to as a Fitting set if it is closed with respect to taking normal subgroups, products of normal ℱ-subgroups, and inner automorphisms of G. A Fitting set ℱ of a group G is said to be π-saturated if H ∈ ℱ for every subgroup H in G such that O π’ (H) ∈ ℱ. In the paper, it is proved that, if ℱ is a π-saturated Fitting set of a π-solvable group G, then there are ℱ-injectors in G and every two of them are conjugate.