Characters and Sylow $3$-subgroup abelianization
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911954704007168 |
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| author | Giannelli, Eugenio Rizo, Noelia Fry, A. A. Schaeffer Vallejo, Carolina |
| author_facet | Giannelli, Eugenio Rizo, Noelia Fry, A. A. Schaeffer Vallejo, Carolina |
| contents | We characterize when a finite group G possesses a Sylow 3-subgroup P with abelianization of order 9 in terms of the number of height zero characters lying in the principal 3-block of G, settling a conjecture put forward by Navarro, Sambale, and Tiep in 2018. Along the way, we show that a recent result by Laradji on the number of character of height zero in a block that lie above a given character of some normal subgroup holds, without any hypothesis on the group for blocks of maximal defect. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characters and Sylow $3$-subgroup abelianization Giannelli, Eugenio Rizo, Noelia Fry, A. A. Schaeffer Vallejo, Carolina Group Theory Representation Theory We characterize when a finite group G possesses a Sylow 3-subgroup P with abelianization of order 9 in terms of the number of height zero characters lying in the principal 3-block of G, settling a conjecture put forward by Navarro, Sambale, and Tiep in 2018. Along the way, we show that a recent result by Laradji on the number of character of height zero in a block that lie above a given character of some normal subgroup holds, without any hypothesis on the group for blocks of maximal defect. |
| title | Characters and Sylow $3$-subgroup abelianization |
| topic | Group Theory Representation Theory |
| url | https://arxiv.org/abs/2405.16665 |