{
  "id": "1801.07197",
  "version": "v1",
  "published": "2018-01-22T17:08:03.000Z",
  "updated": "2018-01-22T17:08:03.000Z",
  "title": "Probabilistically nilpotent groups",
  "authors": [
    "Aner Shalev"
  ],
  "comment": "To appear in Proc. Amer. Math. Soc",
  "categories": [
    "math.GR"
  ],
  "abstract": "We show that, for a finitely generated residually finite group $\\Gamma$, the word $[x_1, \\ldots, x_k]$ is a probabilistic identity of $\\Gamma$ if and only if $\\Gamma$ is virtually nilpotent of class less than $k$. Related results, generalizations and problems are also discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-22T17:08:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E26",
      "20P05"
    ],
    "keywords": [
      "probabilistically nilpotent groups",
      "finitely generated residually finite group",
      "probabilistic identity",
      "virtually nilpotent",
      "related results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}