2023/01/29 by Ping Jin, Lei Wang, Jin, Ping +1
Computer Science · Mathematics · #20C15 #20C20 #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2301.12408
openalex publication_date 2023/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A conjecture raised by Cossey in 2007 asserts that if G is a finite p-solvable group and φ is an irreducible p-Brauer character of G with vertex Q, then the number of lifts of φ is at most |Q:Q'|. This conjecture is now known to be true in several situations for p odd, but there has been little progress for p even. The main obstacle appeared in characteristic two is that all the vertex pairs of a lift are neither linear nor conjugate. In this paper we show that if χ is a lift of an irreducible 2-Brauer character in a solvable group, then χ has a linear Navarro vertex if and only if all the vertex pairs of χ are linear, and in that case all of the twisted vertices of χ are conjugate. Our result can also be used to study other lifting problems of Brauer characters in characteristic two. As an application, we prove a weaker form of Cossey's conjecture for p=2 "one vertex at a time".