{
  "id": "1201.4287",
  "version": "v2",
  "published": "2012-01-20T13:29:36.000Z",
  "updated": "2015-04-15T14:19:54.000Z",
  "title": "Some Properties of Distal Actions on Locally Compact Groups",
  "authors": [
    "C. R. E. Raja",
    "Riddhi Shah"
  ],
  "comment": "27 pages, main results are revised and improved, some preliminary results are removed and some new results are added, some proofs are revised and some are made shorter",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We consider the actions of (semi)groups on a locally compact group by automorphisms. We show the equivalence of distality and pointwise distality for the actions of a certain class of groups. We also show that a compactly generated locally compact group of polynomial growth has a compact normal subgroup $K$ such that $G/K$ is distal and the conjugacy action of $G$ on $K$ is ergodic; moreover, if $G$ itself is (pointwise) distal then $G$ is Lie projective. We prove a decomposition theorem for contraction groups of an automorphism under certain conditions. We give a necessary and sufficient condition for distality of an automorphism in terms of its contraction group. We compare classes of (pointwise) distal groups and groups whose closed subgroups are unimodular. In particular, we study relations between distality, unimodularity and contraction subgroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-20T13:29:36.000Z",
      "abstract": "We show equivalence of distality and pointwise distality of certain actions. We also show that a compactly generated locally compact group of polynomial growth has a compact normal subgroup K such that G/K is distal and the conjugacy action of G on K is ergodic; moreover, if G itself is (pointwise) distal then G is Lie projective. We prove a decomposition theorem for contraction groups of an automorphism under a certain condition. We give a necessary and sufficient condition for distality of an automorphism in terms of its contraction group. We compare classes of (pointwise) distal groups and groups whose closed subgroups are unimodular. In particular, we study relation between distality, unimodularity and contraction subgroups.",
      "comment": "30 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-15T14:19:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05",
      "22D05",
      "37B05",
      "22D05",
      "22E15",
      "22D45"
    ],
    "keywords": [
      "distal actions",
      "contraction group",
      "properties",
      "compact normal subgroup",
      "compactly generated locally compact group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.4287R"
    }
  }
}