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 Oπ (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.