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

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