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

Abstract

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 ≪ G H . In this work we wants to show a characterization of the saturated formation H , which contain G -strongly the formations S π , NX , N k and U ¨ , respectively.