{
  "id": "2208.14334",
  "version": "v1",
  "published": "2022-08-30T15:18:00.000Z",
  "updated": "2022-08-30T15:18:00.000Z",
  "title": "Graceful Ordering of Abelian Groups",
  "authors": [
    "Mohammad Javaheri"
  ],
  "categories": [
    "math.GR",
    "math.NT"
  ],
  "abstract": "Given a sequence ${\\bf g}: g_0,\\ldots, g_{m}$, in a finite group $G$ with $g_0=1_G$, let ${\\bf \\bar g}: \\bar g_0,\\ldots, \\bar g_{m}$, be the sequence defined by $\\bar g_0=1_G$ and $\\bar g_i=g_{i-1}^{-1}g_i$ for $1\\leq i \\leq m$. We prove that if $G$ is abelian then there exists a sequence ${\\bf g}$ such that each element of $G$ appears exactly twice in each of ${\\bf g}$ and ${\\bf \\bar g}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-30T15:18:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20K01",
      "05E15",
      "05B30",
      "20D15",
      "20F22"
    ],
    "keywords": [
      "abelian groups",
      "graceful ordering",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}