{
  "id": "2212.07830",
  "version": "v1",
  "published": "2022-12-15T13:39:18.000Z",
  "updated": "2022-12-15T13:39:18.000Z",
  "title": "Disjointness with all minimal systems under group actions",
  "authors": [
    "Hui Xu",
    "Xiangdong Ye"
  ],
  "comment": "32pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $G$ be a countable discrete group. We give a necessary and sufficient condition for a transitive $G$-system to be disjoint with all minimal $G$-systems, which implies that if a transitive $G$-system is disjoint with all minimal $G$-systems, then it is $\\infty$-transitive, i.e. $(X^k,G)$ is transitive for all $k\\in\\N$, and has dense minimal points. In addition, we show that any $\\infty$-transitive $G$-system with dense distal points are disjoint with all minimal $G$-systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-15T13:39:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37B05"
    ],
    "keywords": [
      "minimal systems",
      "group actions",
      "disjointness",
      "dense minimal points",
      "transitive"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}