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May 28, 2026Forum of Mathematics Sigma0 citationsOpen Access

Height zero characters and Galois automorphisms

AMAlexander MoretóNRNoelia RizoGSGabriel A. L. Souza

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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Cite This Study

Moretó et al. (2026) studied this question.

synapsesocial.com/papers/6a17dcbb3fad632b0f9d969dhttps://doi.org/10.1017/fms.2026.10233
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