Height zero characters and Galois automorphisms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918524379725824 |
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| author | Moretó, Alexander Rizo, Noelia Souza, Gabriel A. L. |
| author_facet | Moretó, Alexander Rizo, Noelia Souza, Gabriel A. L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18535 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Height zero characters and Galois automorphisms Moretó, Alexander Rizo, Noelia Souza, Gabriel A. L. Representation Theory Group Theory 20C15 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. |
| title | Height zero characters and Galois automorphisms |
| topic | Representation Theory Group Theory 20C15 |
| url | https://arxiv.org/abs/2511.18535 |