{
  "id": "1705.02360",
  "version": "v1",
  "published": "2017-05-05T18:34:07.000Z",
  "updated": "2017-05-05T18:34:07.000Z",
  "title": "Groups in which each subgroup is commensurable with a normal subgroup",
  "authors": [
    "Carlo Casolo",
    "Ulderico Dardano",
    "Silvana Rinauro"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "A group G is a cn-group if for each subgroup H of G there exists a normal subgroup N of G such that the index of both H and N in HN is finite. The class of cn-groups contains properly the classes of core- finite groups and that of groups in which each subgroup has finite index in a normal subgroup. In the present paper it is shown that a cn-group whose periodic images are locally finite is finite-by-abelian-by-finite. Such groups are then described into some details by considering automorphisms of abelian groups. Finally, it is shown that if G is a locally graded group with the property that the above index is bounded independently of H, then G is finite-by-abelian-by-finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-05T18:34:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normal subgroup",
      "abelian groups",
      "finite index",
      "cn-groups contains",
      "finite-by-abelian-by-finite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}