{
  "id": "math/9907128",
  "version": "v1",
  "published": "1999-07-21T03:26:09.000Z",
  "updated": "1999-07-21T03:26:09.000Z",
  "title": "Subgroups of monothetic groups",
  "authors": [
    "Sidney A. Morris",
    "Vladimir Pestov"
  ],
  "comment": "10 pages, LaTeX 2e",
  "journal": "Journal of Group Theory 3 (2000), 407-417.",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "It is shown that every separable abelian topological group is isomorphic with a topological subgroup of a monothetic group (that is, a topological group with a single topological generator). In particular, every separable metrizable abelian group embeds into a metrizable monothetic group. More generally, we describe all topological groups that can be embedded into monothetic groups: they are exactly abelian topological groups of weight $\\leq\\frak c$ covered by countably many translations of every nonempty open subset.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-07-21T03:26:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A05"
    ],
    "keywords": [
      "nonempty open subset",
      "separable metrizable abelian group embeds",
      "separable abelian topological group",
      "single topological generator",
      "metrizable monothetic group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......7128M"
    }
  }
}