{
  "id": "2106.15180",
  "version": "v1",
  "published": "2021-06-29T08:56:37.000Z",
  "updated": "2021-06-29T08:56:37.000Z",
  "title": "Decomposition of locally compact coset spaces",
  "authors": [
    "Colin D. Reid"
  ],
  "comment": "31 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "In a previous article by the author and P. Wesolek, it was shown that a compactly generated locally compact group $G$ admits a finite normal series $(G_i)$ in which the factors are compact, discrete or irreducible in the sense that no closed normal subgroup of $G$ lies properly between $G_{i-1}$ and $G_{i}$. In the present article, we generalize this series to an analogous decomposition of the coset space $G/H$ with respect to closed subgroups, where $G$ is locally compact and $H$ is compactly generated. This time, the irreducible factors are coset spaces $G_{i}/G_{i-1}$ where $G_{i}$ is compactly generated and there is no closed subgroup properly between $G_{i-1}$ and $G_{i}$. Such irreducible coset spaces can be thought of as a generalization of primitive actions of compactly generated locally compact groups; we establish some basic properties and discuss some sources of examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-29T08:56:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D05"
    ],
    "keywords": [
      "locally compact coset spaces",
      "compactly generated locally compact group",
      "decomposition",
      "finite normal series",
      "closed subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}