The uniqueness of vertex pairs in π-separable groups. Issue 7 (3rd July 2023)

• Record Type: Journal Article
• Authors: Wang, Lei; Jin, Ping
• Is Part Of: Communications in algebra. Volume 51:Issue 7(2023)
• Page Start: 3060
• Page End: 3065
• Publication Date: 2023-07-03
• Subjects: Lifts -- twisted vertices -- vertex pairs -- π-factored characters -- π-partial characters; Primary: 20C15 -- Secondary: 20C20; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2023.2177045
• Languages: English
• ISSNs: 0092-7872

Abstract

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.