{
  "id": "1012.1653",
  "version": "v1",
  "published": "2010-12-08T00:34:11.000Z",
  "updated": "2010-12-08T00:34:11.000Z",
  "title": "Algorithmically finite groups",
  "authors": [
    "A. Myasnikov",
    "D. Osin"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We call a group $G$ {\\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their properties. For instance, we show that the Equality Problem is decidable in our groups only on strongly (exponentially) negligible sets of inputs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-12-08T00:34:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65"
    ],
    "keywords": [
      "infinite algorithmically finite groups",
      "infinite set",
      "pairwise distinct elements",
      "construct examples",
      "equality problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.1653M"
    }
  }
}