Lifts of Brauer characters in characteristic two, II

Abstract

In 2007, J. P. Cossey conjectured that if $G$ is a finite $p$-solvable group and $\varphi$ is an irreducible Brauer character of $G$ with vertex $Q$, then the number of lifts of $\varphi$ is at most $|Q:Q'|$. In this paper we revisited Cossey's conjecture for $p=2$ from the perspective of Navarro vertices and obtained a new way to count the number of lifts of $\varphi$. Some applications were given.