{
  "id": "1811.02115",
  "version": "v1",
  "published": "2018-11-03T16:12:22.000Z",
  "updated": "2018-11-03T16:12:22.000Z",
  "title": "Examples of defining groups by finite automata",
  "authors": [
    "Victoriia Korchemna"
  ],
  "comment": "13 pages, 6 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We construct the groups $<A,B,C \\;| \\, A^2,B^2,C^2,(ABC)^2>$ and $<A,B \\;| \\, A^2,B^4,(AB)^4>$, using 3-state automata over the alphabets $\\{1,2,3\\}$ and $\\{1,2,3,4\\}$. In addition, we show, how to define direct powers of $G$ by automaton (when for $G$ it's given), keeping the alphabet.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-03T16:12:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "20E08"
    ],
    "keywords": [
      "finite automata",
      "defining groups",
      "define direct powers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}