On Normal Intersection Conjugacy Functions in Finite Groups

Abstract

In the present paper, we investigate conjugacy classes of subgroups of a fixed but arbitrary group where the definition of these subgroups is made entirely within the structure of the group. We have shown that these subgroups are analogous to F-injectors of the group where F is a locally defined Fitting class, but preclude the existence of such a class in their definition. Moreover, the subgroups used to define the subgroups of such a conjugacy class are analogous to the F(p)-radicals of the group.