Beyond graph products and cactus groups: quandle products of groups
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909610364895232 |
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| author | Genevois, Anthony |
| author_facet | Genevois, Anthony |
| contents | In this paper, we introduce and initiate the study of quandle products of groups, a family of groups that includes graph products of groups, cactus groups, wreath products, and the recently introduced trickle groups. Our approach is geometric: we show that quandle products admit quasi-median Cayley graphs; and, then, we exploit this geometry to deduce various valuable information about quandle products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09194 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Beyond graph products and cactus groups: quandle products of groups Genevois, Anthony Group Theory Metric Geometry 20F65, 20F10, 20E22, 05C25 In this paper, we introduce and initiate the study of quandle products of groups, a family of groups that includes graph products of groups, cactus groups, wreath products, and the recently introduced trickle groups. Our approach is geometric: we show that quandle products admit quasi-median Cayley graphs; and, then, we exploit this geometry to deduce various valuable information about quandle products. |
| title | Beyond graph products and cactus groups: quandle products of groups |
| topic | Group Theory Metric Geometry 20F65, 20F10, 20E22, 05C25 |
| url | https://arxiv.org/abs/2505.09194 |