What does this research mean for the field?

A strengthened version of Brauer's height zero conjecture holds for the principal p-block of a finite group when accounting for the action of specific Galois automorphisms. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This paper aims to strengthen Brauer's height zero conjecture for finite groups by incorporating Galois automorphisms.

May 28, 2026Open Access

Height zero characters and Galois automorphisms

Key Points

This paper aims to strengthen Brauer's height zero conjecture for finite groups by incorporating Galois automorphisms.
Analyses the principal p-block of the finite group G.
Considers the action of a specific group of Galois automorphisms.
Develops a structural result analogous to the Itô–Michler theorem.
Provides a strengthened version of Brauer's height zero conjecture for the principal p-block of G.
Establishes a new structural result in the context of Galois automorphisms.

Abstract

Abstract Let G be a finite group and let p be a prime. In this paper, we prove a strengthened version of Brauer’s height zero conjecture for the principal p -block of G that takes the action of a certain group of Galois automorphisms into account. This answers a conjecture recently proposed by Malle, Moretó, Rizo and Schaeffer Fry. We then use this to obtain a structural result which can be seen as a Galois version of the Itô–Michler theorem.

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