Let π be a set of prime numbers and G a finite π-separable group. Let θ be an irreducible π~'-partial character of a normal subgroup N of G and denote by I_π~' (G|θ), the set of all irreducible π~'-partial characters ψ of G such that θ is a constituent of ψ _N. In this paper, we obtain some information about the vertices of the elements in I_π~' (G|θ). 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.
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