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- W4382363857 abstract "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 might be 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”." @default.
- W4382363857 created "2023-06-29" @default.
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- W4382363857 date "2023-11-01" @default.
- W4382363857 modified "2023-10-12" @default.
- W4382363857 title "Lifts of Brauer characters in characteristic two" @default.
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- W4382363857 doi "https://doi.org/10.1016/j.jalgebra.2023.05.048" @default.
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