{
  "id": "1812.10554",
  "version": "v1",
  "published": "2018-12-03T19:06:41.000Z",
  "updated": "2018-12-03T19:06:41.000Z",
  "title": "A short note on conjugacy class racks",
  "authors": [
    "Selçuk Kayacan"
  ],
  "comment": "2 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a finite $p$-group and $C$ be a conjugacy class of $G$. We prove that the order complex of the subrack poset of $C$ is homotopy equivalent to a $(m-2)$-sphere, where $m$ is the number of maximal elements in the subrack poset.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-03T19:06:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "conjugacy class racks",
      "short note",
      "subrack poset",
      "homotopy equivalent",
      "order complex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 2,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}