{
  "id": "1505.03462",
  "version": "v1",
  "published": "2015-05-13T17:24:46.000Z",
  "updated": "2015-05-13T17:24:46.000Z",
  "title": "Classification of finite groups with toroidal or projective-planar permutability graphs",
  "authors": [
    "R. Rajkumar",
    "P. Devi",
    "Andrei Gagarin"
  ],
  "comment": "30 pages, 8 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G$ be a group. The permutability graph of subgroups of $G$, denoted by $\\Gamma(G)$, is a graph having all the proper subgroups of $G$ as its vertices, and two subgroups are adjacent in $\\Gamma(G)$ if and only if they permute. In this paper, we classify the finite groups whose permutability graphs are toroidal or projective-planar. In addition, we classify the finite groups whose permutability graph does not contain one of $K_{3,3}$, $K_{1,5}$, $C_6$, $P_5$, or $P_6$ as a subgraph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-13T17:24:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C10"
    ],
    "keywords": [
      "finite groups",
      "projective-planar permutability graphs",
      "classification",
      "proper subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150503462R"
    }
  }
}