Let G be a finite group, let p be an odd prime, and let P Î Sylp(G). If NG(P) = PCG(P), then there is a canonical correspondence between the irreducible complex characters of G of degree not divisible by p belonging to the principal block of G and the linear characters of P. As a consequence, we give a characterization of finite groups that possess a self-normalizing Sylow p-subgroup or a p-decomposable Sylow normalizer.
- McKay conjecture
- P-decomposable Sylow normalizer
- Self-normalizing Sylow subgroup
ASJC Scopus subject areas
- Algebra and Number Theory