Lifts and twisted vertices in solvable groups

Let [Formula: see text] be a finite [Formula: see text]-solvable group, and let [Formula: see text] be an irreducible complex character that is a lift of some [Formula: see text]-Brauer character of [Formula: see text]. For [Formula: see text], Cossey and Lewis established certain conditions to guarantee that all irreducible constituents of [Formula: see text] are lifts for every normal subgroup [Formula: see text] of [Formula: see text]. In this paper, we established analogous results for [Formula: see text] by using twisted vertices.