Galois action on the principal block and generation of Sylow 3-subgroups
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910023376961536 |
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| author | Ketchum, Eden Martínez, J. Miquel Rizo, Noelia Fry, A. A. Schaeffer |
| author_facet | Ketchum, Eden Martínez, J. Miquel Rizo, Noelia Fry, A. A. Schaeffer |
| contents | In this paper, we prove one direction of a conjecture of Navarro-Rizo-Schaeffer Fry-Vallejo positing an algorithm to determine from the character table whether a finite group has $2$-generated Sylow $3$-subgroups. This gives further evidence of the blockwise version of the Galois-McKay conjecture (also known as the Alperin-McKay-Navarro conjecture). A key step involves proving the Isaacs-Navarro Galois conjecture for principal blocks for finite groups with a certain structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14366 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Galois action on the principal block and generation of Sylow 3-subgroups Ketchum, Eden Martínez, J. Miquel Rizo, Noelia Fry, A. A. Schaeffer Group Theory Representation Theory 20C15, 20D20 In this paper, we prove one direction of a conjecture of Navarro-Rizo-Schaeffer Fry-Vallejo positing an algorithm to determine from the character table whether a finite group has $2$-generated Sylow $3$-subgroups. This gives further evidence of the blockwise version of the Galois-McKay conjecture (also known as the Alperin-McKay-Navarro conjecture). A key step involves proving the Isaacs-Navarro Galois conjecture for principal blocks for finite groups with a certain structure. |
| title | Galois action on the principal block and generation of Sylow 3-subgroups |
| topic | Group Theory Representation Theory 20C15, 20D20 |
| url | https://arxiv.org/abs/2602.14366 |