{
  "id": "0807.3102",
  "version": "v2",
  "published": "2008-07-19T15:10:31.000Z",
  "updated": "2009-07-22T12:58:50.000Z",
  "title": "The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups",
  "authors": [
    "Oleg V. Gutik",
    "Dušan Pagon",
    "Dušan Repovš"
  ],
  "journal": "Acta Math. Hungarica 124:3 (2009), 201-214",
  "doi": "10.1007/s10474-009-8144-8",
  "categories": [
    "math.GN",
    "math.GR"
  ],
  "abstract": "In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e. the union of all maximal subgroups) of the semigroup $S$ is a closed subset in $S$; (iii) the inversion $\\operatorname{inv}\\colon H(S)\\to H(S)$ is continuous; and (iv) the projection $\\pi\\colon H(S)\\to E(S)$, $\\pi\\colon x\\longmapsto xx^{-1}$, onto the subset of idempotents $E(S)$ of $S$, is continuous.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-22T12:58:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A15",
      "54D55",
      "54H10",
      "20M10"
    ],
    "keywords": [
      "countably compact topological semigroups",
      "maximal subgroup",
      "continuity",
      "clifford part",
      "idempotents"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.3102G"
    }
  }
}