{
  "id": "1707.03066",
  "version": "v1",
  "published": "2017-07-10T21:19:34.000Z",
  "updated": "2017-07-10T21:19:34.000Z",
  "title": "On expansions of non-abelian free groups by cosets of a finite index subgroup",
  "authors": [
    "Javier de la Nuez González"
  ],
  "comment": "PhD Thesis",
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "Let $F$ be a finitely generated non-abelian free group and $Q$ a finite quotient. Denote by $L_Q$ the language obtained by adding unary predicates $P_q$, $q\\in Q$ to the language of groups. Using a slight generalization of some of the techniques involved in Zlil Sela's solution to Tarski\\'s problem on the elementary theory of non-abelian free groups, we provide a few basic results on the validity of first order entences in the $L_Q$-expansion of $F$ in which every $P_q$ is interpreted as the preimage of $q$ in $F$. In particular we prove an analogous result to Sela's generalization of Merzlyakov's theorem on $\\forall\\exists$-sentences and show that the positive theory depends only on $Q$ and neither on the rank of $F$ nor the particular quotient map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-10T21:19:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05",
      "20F65",
      "03Cxx"
    ],
    "keywords": [
      "finite index subgroup",
      "zlil selas solution",
      "first order entences",
      "finitely generated non-abelian free group",
      "merzlyakovs theorem"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}