The uniqueness of vertex pairs in π-separable groups. Issue 7 (3rd July 2023) - Wang, Lei
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 2 ∈ π, but the result can fail for 2 ∉ π . In this paper we introduce the notion of the linear twisted vertices in the case where 2 ∉ π, and then establish the uniqueness for such vertices under the conditions that either χ is an N -lift for a π -chain N of G or it has a linear Navarro vertex, thus answering a question proposed by them.