{
  "id": "0704.3911",
  "version": "v1",
  "published": "2007-04-30T09:55:50.000Z",
  "updated": "2007-04-30T09:55:50.000Z",
  "title": "Distal actions and ergodic actions on compact groups",
  "authors": [
    "C. R. E. Raja"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $K$ be a compact metrizable group and $\\Ga$ be a group of automorphisms of $K$. We first show that each $\\ap \\in \\Ga$ is distal on $K$ implies $\\Ga$ itself is distal on $K$, a local to global correspondence provided $\\Ga$ is a generalized $\\ov{FC}$-group or $K$ is a connected finite-dimensional group. We show that $\\Ga$ contains an ergodic automorphism when $\\Ga$ is nilpotent and ergodic on a connected finite-dimensional compact abelian group $K$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-30T09:55:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "37A15",
      "22B05",
      "22C05"
    ],
    "keywords": [
      "compact groups",
      "ergodic actions",
      "distal actions",
      "connected finite-dimensional compact abelian group",
      "finite-dimensional group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3911R"
    }
  }
}