The G-strong containment for locally defined formations of finite soluble groups

Let F and H be two saturated formations of finite soluble groups, with canonical definition F and H, respectively, and Char(F)⊆Char(H). We say that F is G-strong containment in H, when for all p∈Char(F) and for all H∈H the H(p)-Residual of H is in a F-projector E of H containment. In this case we write F≪GH. In this work we wants to show a characterization of the saturated formation H, which contain G-strongly the formations Sπ, NX, Nk and , respectively.