{
  "id": "2505.09194",
  "version": "v1",
  "published": "2025-05-14T06:55:57.000Z",
  "updated": "2025-05-14T06:55:57.000Z",
  "title": "Beyond graph products and cactus groups: quandle products of groups",
  "authors": [
    "Anthony Genevois"
  ],
  "comment": "50 pages, 26 figures. Comments are welcome!",
  "categories": [
    "math.GR",
    "math.MG"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-14T06:55:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20F10",
      "20E22",
      "05C25"
    ],
    "keywords": [
      "graph products",
      "cactus groups",
      "quandle products admit quasi-median cayley",
      "products admit quasi-median cayley graphs",
      "trickle groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 50,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}