{
  "id": "1511.07021",
  "version": "v1",
  "published": "2015-11-22T15:12:03.000Z",
  "updated": "2015-11-22T15:12:03.000Z",
  "title": "Minimality of the Semidirect Product",
  "authors": [
    "Michael Megrelishvili",
    "Luie Polev",
    "Menachem Shlossberg"
  ],
  "comment": "13 pages. arXiv admin note: substantial text overlap with arXiv:1501.03410",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "A topological group is minimal if it does not admit a strictly coarser Hausdorff group topology. We prove that for a compact topological group $G$, the semidirect product $G\\leftthreetimes P$ is minimal for every closed subgroup $P$ of $Aut(G)$. In general, the compactness of $G$ is essential; $G\\leftthreetimes P$ might be nonminimal even for precompact minimal groups $G$ as it follows from an example of Eberhardt-Dierolf-Schwanengel. Some of the results were inspired by a work of Gamarnik .",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-22T15:12:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semidirect product",
      "minimality",
      "strictly coarser hausdorff group topology",
      "precompact minimal groups",
      "compact topological group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}