Abstract
Let G be a finite π-separable group, where π is a set of primes, and let χ be an irreducible complex character that is a π-lift of some π-partial character of G. It was proved by Cossey and Lewis that all of the vertex pairs for χ are linear and conjugate in G if , but the result can fail for . In this paper we introduce the notion of the linear twisted vertices in the case where , and then establish the uniqueness for such vertices under the conditions that either χ is an -lift for a π-chain of G or it has a linear Navarro vertex, thus answering a question proposed by them.
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