{
  "id": "2102.04598",
  "version": "v1",
  "published": "2021-02-09T01:35:40.000Z",
  "updated": "2021-02-09T01:35:40.000Z",
  "title": "Isolated subgroups of finite abelian groups",
  "authors": [
    "Marius Tărnăuceanu"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We say that a subgroup $H$ is isolated in a group $G$ if for every $x\\in G$ we have either $x\\in H$ or $\\langle x\\rangle\\cap H=1$. In this short note, we describe the set of isolated subgroups of a finite abelian group. The technique used is based on an interesting connection between isolated subgroups and the function sum of element orders of a finite group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-09T01:35:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite abelian group",
      "isolated subgroups",
      "function sum",
      "finite group",
      "element orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}