Lifts of Brauer characters and vertex pairs for odd primes

Abstract

Let $p$ be an odd prime, let $G$ be a finite $p$-solvable group, and let $φ\in\IBr_p(G)$ have vertex $Q$. We prove that $φ$ has at most $|Q:Q'|$ lifts to ordinary irreducible characters, establishing Cossey's conjecture for odd primes.