Latin quandles of size $16p$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908561002463232 |
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| author | Bonatto, Marco Spaggiari, Filippo |
| author_facet | Bonatto, Marco Spaggiari, Filippo |
| contents | In this paper we obtain the classification of latin quandles of size $16p$ where $p$ is an odd prime. In particular we have that such quandles are always subdirectly reducible but in some cases for small primes. Specifically, we have that latin quandles of size $16p$ are affine if $p\neq 1 \pmod{3}$ or $p\neq 3,5$. If $p=1\pmod 3$ there are $2$ subdirectly reducible non directly decomposable latin quandles of size $16p$ for every prime with $p=1\pmod{3}$ and there are one subdirectly irreducible latin quandle of size $16p$ for $p=3,5$. We provide explicit constructions as coset quandles for all the quandles mentioned above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Latin quandles of size $16p$ Bonatto, Marco Spaggiari, Filippo Group Theory 57K12 In this paper we obtain the classification of latin quandles of size $16p$ where $p$ is an odd prime. In particular we have that such quandles are always subdirectly reducible but in some cases for small primes. Specifically, we have that latin quandles of size $16p$ are affine if $p\neq 1 \pmod{3}$ or $p\neq 3,5$. If $p=1\pmod 3$ there are $2$ subdirectly reducible non directly decomposable latin quandles of size $16p$ for every prime with $p=1\pmod{3}$ and there are one subdirectly irreducible latin quandle of size $16p$ for $p=3,5$. We provide explicit constructions as coset quandles for all the quandles mentioned above. |
| title | Latin quandles of size $16p$ |
| topic | Group Theory 57K12 |
| url | https://arxiv.org/abs/2509.22145 |