{
  "id": "1907.05968",
  "version": "v1",
  "published": "2019-07-12T21:52:43.000Z",
  "updated": "2019-07-12T21:52:43.000Z",
  "title": "Local to global property in free groups",
  "authors": [
    "Ofir David"
  ],
  "comment": "4 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "The local to global property for an equation $\\psi$ over a group G asks to show that $\\psi$ is solvable in G if and only if it is solvable in every finite quotient of G. In this paper we focus that in order to prove this local to global property for free groups $G=F_k$, it is enough to prove for k less or equal the number of parameters in $\\psi$. In particular we use it to show that the local to global property holds for m-powers in free groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-12T21:52:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05",
      "20E18",
      "20F34"
    ],
    "keywords": [
      "free groups",
      "global property holds",
      "finite quotient",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}