A Brauer--Galois height zero conjecture
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910342990266368 |
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| author | Malle, Gunter Moretó, Alexander Rizo, Noelia Fry, A. A. Schaeffer |
| author_facet | Malle, Gunter Moretó, Alexander Rizo, Noelia Fry, A. A. Schaeffer |
| contents | Recently, Malle and Navarro obtained a Galois strengthening of Brauer's height zero conjecture for principal $p$-blocks when $p=2$, considering a particular Galois automorphism of order~$2$. In this paper, for any prime $p$ we consider a certain elementary abelian $p$-subgroup of the absolute Galois group and propose a Galois version of Brauer's height zero conjecture for principal $p$-blocks. We prove it when $p=2$ and also for arbitrary $p$ when $G$ does not involve certain groups of Lie type of small rank as composition factors. Furthermore, we prove it for almost simple groups and for $p$-solvable groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Brauer--Galois height zero conjecture Malle, Gunter Moretó, Alexander Rizo, Noelia Fry, A. A. Schaeffer Representation Theory Group Theory 20C15, 20C20, 20C33 Recently, Malle and Navarro obtained a Galois strengthening of Brauer's height zero conjecture for principal $p$-blocks when $p=2$, considering a particular Galois automorphism of order~$2$. In this paper, for any prime $p$ we consider a certain elementary abelian $p$-subgroup of the absolute Galois group and propose a Galois version of Brauer's height zero conjecture for principal $p$-blocks. We prove it when $p=2$ and also for arbitrary $p$ when $G$ does not involve certain groups of Lie type of small rank as composition factors. Furthermore, we prove it for almost simple groups and for $p$-solvable groups. |
| title | A Brauer--Galois height zero conjecture |
| topic | Representation Theory Group Theory 20C15, 20C20, 20C33 |
| url | https://arxiv.org/abs/2402.08361 |