A normal version of Brauer’s height zero conjecture
Abstract
Abstract The celebrated Itô–Michler theorem asserts that a prime p does not divide the degree of any irreducible character of a finite group G if and only if G has a normal and abelian Sylow p -subgroup. The principal block case of the recently-proven Brauer’s height zero conjecture isolates the abelian part in the Itô–Michler theorem. In this paper, we show that the normal part can also be isolated in a similar way. This is a consequence of work on a strong form of the so-called Brauer’s height zero conjecture for two primes of Malle and Navarro. Using our techniques, we also provide an alternate proof of this conjecture.
Fields of Study & Subjects
Mathematics and Applications
Graph theory and applications
Point processes and geometric inequalities
Publication details
- Journal / source
- Mathematische Annalen
- Publisher
- Springer Science and Business Media LLC
- Volume
- 395
- Issue
- 2
- Publication date
- 17 April 2026
- Language
- EN