Primitive quandles with alternating displacement group
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909317626593280 |
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| author | Cvrček, Milan Stanovský, David |
| author_facet | Cvrček, Milan Stanovský, David |
| contents | We classify primitive quandles with alternating displacement group. All of them are conjugation quandles, and the following is a complete list of the underlying conjugacy classes: transpositions in $S_n$ for $n=3$ and $n\geq5$; fixpoint-free involutions in $S_n$ for $n\equiv 2\pmod 4$, $n\geq6$; fixpoint-free involutions in $A_n$ for $n\equiv 0\pmod 4$, $n\geq12$; and one exceptional conjugacy class of size 36 in a group of order 720. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15642 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Primitive quandles with alternating displacement group Cvrček, Milan Stanovský, David Group Theory 57K12, 20N02, 20B15 We classify primitive quandles with alternating displacement group. All of them are conjugation quandles, and the following is a complete list of the underlying conjugacy classes: transpositions in $S_n$ for $n=3$ and $n\geq5$; fixpoint-free involutions in $S_n$ for $n\equiv 2\pmod 4$, $n\geq6$; fixpoint-free involutions in $A_n$ for $n\equiv 0\pmod 4$, $n\geq12$; and one exceptional conjugacy class of size 36 in a group of order 720. |
| title | Primitive quandles with alternating displacement group |
| topic | Group Theory 57K12, 20N02, 20B15 |
| url | https://arxiv.org/abs/2401.15642 |