{
  "id": "2211.08699",
  "version": "v1",
  "published": "2022-11-16T06:22:56.000Z",
  "updated": "2022-11-16T06:22:56.000Z",
  "title": "Upper Bounds For The Diameter Of A Direct Power Of Solvable Groups",
  "authors": [
    "Azizollah Azad",
    "Nasim Karimi"
  ],
  "comment": "10 pages. arXiv admin note: substantial text overlap with arXiv:1506.02695",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let G be a finite group with a generating set A. By the (symmetric) diameter of G with respect to A we mean the maximum over g in G of the length of the shortest word in (A union A inverse)A expressing g.By the (symmetric) diameter of G we mean the maximum of (symmetric) diameter over all generating sets of G. Let n greater than or equal to 1, by G power n we mean the n-th direct power of G. For n greater than or equal to 1 and finite non-abelian solvable group G we find an upper bound, growing polynomially with respect to n, for the symmetric diameter and the diameter of G power n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-16T06:22:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "upper bound",
      "generating set",
      "finite non-abelian solvable group",
      "n-th direct power",
      "finite group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}