Associated groups of symmetric quandles
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866918120196669440 |
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| author | Akita, Toshiyuki Shikata, Kakeru |
| author_facet | Akita, Toshiyuki Shikata, Kakeru |
| contents | In this paper, we investigate the structure of associated groups of symmetric quandles. Among other results, we explore the relationship between the associated group of a symmetric quandle and that of its underlying quandle. We provide a group-theoretic characterization of associated groups of symmetric quandles. Furthermore, we show that a symmetric quandle is embeddable if and only if its underlying quandle is embeddable, and we determine the abelianization of these associated groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Associated groups of symmetric quandles Akita, Toshiyuki Shikata, Kakeru Geometric Topology Group Theory Primary 20F05, 20N02, Secondary 08A05, 19C09, 57K12 In this paper, we investigate the structure of associated groups of symmetric quandles. Among other results, we explore the relationship between the associated group of a symmetric quandle and that of its underlying quandle. We provide a group-theoretic characterization of associated groups of symmetric quandles. Furthermore, we show that a symmetric quandle is embeddable if and only if its underlying quandle is embeddable, and we determine the abelianization of these associated groups. |
| title | Associated groups of symmetric quandles |
| topic | Geometric Topology Group Theory Primary 20F05, 20N02, Secondary 08A05, 19C09, 57K12 |
| url | https://arxiv.org/abs/2505.23507 |