Hayashi Property for Conjugation Quandles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917969618010112 |
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| author | Filipi, Filip |
| author_facet | Filipi, Filip |
| contents | We give a comprehensive description of conjugation quandles and their connectedness. In this context, we find a characterization of Hayashi's conjecture (2013) in terms of a centrality condition of groups. This condition is thus a conjecture itself and it states that powers of elements of a finite and generating conjugacy classes should be central whenever they commute with one particular element of this class. We prove this condition in several cases, e.g. for finite nilpotent, symmetric, alternating, and dihedral groups. All of these results translate to Hayashi's conjecture for the corresponding conjugation quandles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_22377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hayashi Property for Conjugation Quandles Filipi, Filip Group Theory 20E34, 20E45, 20N02, 57K12 We give a comprehensive description of conjugation quandles and their connectedness. In this context, we find a characterization of Hayashi's conjecture (2013) in terms of a centrality condition of groups. This condition is thus a conjecture itself and it states that powers of elements of a finite and generating conjugacy classes should be central whenever they commute with one particular element of this class. We prove this condition in several cases, e.g. for finite nilpotent, symmetric, alternating, and dihedral groups. All of these results translate to Hayashi's conjecture for the corresponding conjugation quandles. |
| title | Hayashi Property for Conjugation Quandles |
| topic | Group Theory 20E34, 20E45, 20N02, 57K12 |
| url | https://arxiv.org/abs/2503.22377 |