{
  "id": "2407.16440",
  "version": "v1",
  "published": "2024-07-23T12:49:11.000Z",
  "updated": "2024-07-23T12:49:11.000Z",
  "title": "Finite central extensions of o-minimal groups",
  "authors": [
    "Elías Baro",
    "Daniel Palacín"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We answer in the affirmative a conjecture of Berarducci, Peterzil and Pillay \\cite{BPP10} for solvable groups, which is an o-minimal version of a particular case of Milnor's isomorphism conjecture \\cite{jM83}. We prove that every finite central extension of a definably connected solvable definable group in an o-minimal structure is equivalent to a finite central extension which is definable without additional parameters. The proof relies on an o-minimal adaptation of the higher inflation-restriction exact sequence due to Hochschild and Serre. As in \\cite{jM83}, we also prove in o-minimal expansions of real closed fields that the conjecture reduces to definably simple groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-23T12:49:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite central extension",
      "o-minimal groups",
      "connected solvable definable group",
      "higher inflation-restriction exact sequence",
      "milnors isomorphism conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}