{
  "id": "1303.1364",
  "version": "v1",
  "published": "2013-03-06T15:51:12.000Z",
  "updated": "2013-03-06T15:51:12.000Z",
  "title": "On the tensor degree of finite groups",
  "authors": [
    "Peyman Niroomand",
    "Francesco G. Russo"
  ],
  "comment": "10 pages, accepted in Ars Combinatoria with revisions",
  "categories": [
    "math.GR",
    "math.AT",
    "math.CO"
  ],
  "abstract": "We study the number of elements $x$ and $y$ of a finite group $G$ such that $x \\otimes y= 1_{_{G \\otimes G}}$ in the nonabelian tensor square $G \\otimes G$ of $G$. This number, divided by $|G|^2$, is called the tensor degree of $G$ and has connection with the exterior degree, introduced few years ago in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343]. The analysis of upper and lower bounds of the tensor degree allows us to find interesting structural restrictions for the whole group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-03-06T15:51:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15",
      "20J99",
      "20D60",
      "20C25"
    ],
    "keywords": [
      "finite group",
      "tensor degree",
      "exterior degree",
      "nonabelian tensor square",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.1364N"
    }
  }
}