{
  "id": "1810.11346",
  "version": "v1",
  "published": "2018-10-26T14:27:07.000Z",
  "updated": "2018-10-26T14:27:07.000Z",
  "title": "Lattices of finite abelian groups",
  "authors": [
    "Frieder Ladisch"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT",
    "math.MG"
  ],
  "abstract": "We study certain lattices constructed from finite abelian groups. We show that such a lattice is eutactic, thereby confirming a conjecture by B\\\"ottcher, Eisenbarth, Fukshansky, Garcia, Maharaj. Our methods also yield simpler proofs of two known results: First, such a lattice is strongly eutactic if and only if the abelian group has odd order or is elementary abelian. Second, such a lattice has a basis of minimal vectors, except for the cyclic group of order 4.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-26T14:27:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11H31",
      "11H55"
    ],
    "keywords": [
      "finite abelian groups",
      "yield simpler proofs",
      "odd order",
      "minimal vectors",
      "cyclic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}