Vertices of simple modules and normal subgroups ofp-solvable groups

Abstract

Let π be a set of prime numbers andG a finite π-separable group. Let θ be an irreducible π′-partial character of a normal subgroupN ofG and denote by I_π′ (G‖θ), the set of all irreducible π′-partial characters Φ ofG such that θ is a constituent of Φ_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 characteristicsp) of a finitep-solvable group lying over a fixed simple module of a normal subgroup.