On minimal positive heights for blocks of almost quasi-simple groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912095693438976 |
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| author | Malle, Gunter Fry, A. A. Schaeffer |
| author_facet | Malle, Gunter Fry, A. A. Schaeffer |
| contents | The Eaton--Moretó conjecture extends the recently-proven Brauer height zero conjecture to blocks with non-abelian defect group, positing equality between the minimal positive heights of a block of a finite group and its defect group. Here we provide further evidence for the inequality in this conjecture that is not implied by Dade's conjecture. Specifically, we consider minimal counter-examples and show that these cannot be found among almost quasi-simple groups for $p\ge5$. Along the way, we observe that most such blocks have minimal positive height equal to~1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22745 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On minimal positive heights for blocks of almost quasi-simple groups Malle, Gunter Fry, A. A. Schaeffer Representation Theory Group Theory 20C15, 20C20, 20C33 The Eaton--Moretó conjecture extends the recently-proven Brauer height zero conjecture to blocks with non-abelian defect group, positing equality between the minimal positive heights of a block of a finite group and its defect group. Here we provide further evidence for the inequality in this conjecture that is not implied by Dade's conjecture. Specifically, we consider minimal counter-examples and show that these cannot be found among almost quasi-simple groups for $p\ge5$. Along the way, we observe that most such blocks have minimal positive height equal to~1. |
| title | On minimal positive heights for blocks of almost quasi-simple groups |
| topic | Representation Theory Group Theory 20C15, 20C20, 20C33 |
| url | https://arxiv.org/abs/2410.22745 |