Abstract
Let pi be a set of prime numbers and G a finite pi-separable group. Let theta be an irreducible pi-partial character of a normal subgroup N of G and denote by I-pi' (G\theta), the set of all irreducible pi'-partial characters V of G such that theta is a constituent Of partial derivative(N). In this paper, we obtain some information about the vertices of the elements in I-pi' (G\theta). As a consequence, we establish an analogue of Fong's theorem on defect groups of covering blocks, for the vertices of the simple modules (in characteristic p) of a finite p-solvable group lying over a fixed simple module of a normal subgroup.