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arXiv · 2511.18535

Height zero characters and Galois automorphisms

Alexander Moretó·Noelia Rizo·Gabriel A. L. Souza
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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, Moret\'o, Rizo and Schaeffer Fry. We then use this to obtain a structural result which can be seen as a Galois version of the It\^o-Michler theorem.

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BibTeXRIS

Alexander Moretó, Noelia Rizo, Gabriel A. L. Souza. 2025-11-23. Height zero characters and Galois automorphisms. https://doi.org/10.1017/fms.2026.10233

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