{
  "id": "2206.05677",
  "version": "v1",
  "published": "2022-06-12T06:39:22.000Z",
  "updated": "2022-06-12T06:39:22.000Z",
  "title": "On groups interpretable in various valued fields",
  "authors": [
    "Yatir Halevi",
    "Assaf Hasson",
    "Ya'acov Peterzil"
  ],
  "categories": [
    "math.LO",
    "math.GR"
  ],
  "abstract": "We study infinite groups interpretable in $V$-minimal, power bounded $T$-convex or certain expansions of $p$-adically closed fields. We show that every such group $G$ has unbounded exponent and if $G$ is dp-minimal then it is abelian-by-finite. Along the way, we associate with any infinite interpretable group an infinite type-definable subgroup which is definably isomorphic to a group in one of four distinguished sorts: the underlying valued field $K$, its residue field $\\textbf{k}$ (when infinite), its value group $\\Gamma$, or $K/\\mathcal{O}$, where $\\mathcal{O}$ is the valuation ring. Our work uses and extends techniques developed in [8] to circumvent elimination of imaginaries.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-12T06:39:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "valued field",
      "infinite interpretable group",
      "infinite type-definable subgroup",
      "study infinite groups interpretable",
      "residue field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}