{
  "id": "0904.0848",
  "version": "v1",
  "published": "2009-04-06T05:51:45.000Z",
  "updated": "2009-04-06T05:51:45.000Z",
  "title": "On the existence of ergodic automorphisms in ergodic ${\\mathbb Z} ^d$-actions on compact groups",
  "authors": [
    "C. R. E. Raja"
  ],
  "categories": [
    "math.DS",
    "math.RT"
  ],
  "abstract": "Let $K$ be a compact metrizable group and $\\Ga$ be a finitely generated group of commuting automorphisms of $K$. We show that ergodicity of $\\Ga$ implies $\\Ga$ contains ergodic automorphisms if center of the action, $Z(\\Ga) = \\{\\ap \\in {\\rm Aut}(K) \\mid \\ap {\\rm commutes with elements of \\rm} \\Ga \\}$ has DCC. To explain that the condition on the center of the action is not restrictive, we discuss certain abelian groups which in particular, retrieves Theorems of Berend \\cite{Be} and Schmidt \\cite{Sc1} proved in this context.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-06T05:51:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A15",
      "37B05"
    ],
    "keywords": [
      "compact groups",
      "contains ergodic automorphisms",
      "abelian groups",
      "compact metrizable group",
      "retrieves theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.0848R"
    }
  }
}