On the theory of F-centrality of chief factors and F-hypercentre for Fitting classes

In this paper, we establish the theory of F-centrality of chief factors and F-hypercentre for Fitting classes. Based on this, we prove that every F-injector of G covers each F-central chief factor of G and avoids each F-eccentric chief factor of G if the Fitting class F has an integrated and invariable H-function. As an application, we also give a new method to define local Fitting classes, that is, we use local functions but not H-functions to define local Fitting classes.