{
  "id": "1005.5222",
  "version": "v1",
  "published": "2010-05-28T06:22:35.000Z",
  "updated": "2010-05-28T06:22:35.000Z",
  "title": "Degenerations and orbits in finite abelian groups",
  "authors": [
    "Kunal Dutta",
    "Amritanshu Prasad"
  ],
  "comment": "14 pages, 5 figures",
  "journal": "Journal of Combinatorial Theory, Series A, Volume 118, Issue 6, August 2011, Pages 1685-1694",
  "doi": "10.1016/j.jcta.2011.02.002",
  "categories": [
    "math.GR",
    "math.CO",
    "math.NT"
  ],
  "abstract": "A notion of degeneration of elements in groups is introduced. It is used to parametrize the orbits in a finite abelian group under its full automorphism group by a finite distributive lattice. A pictorial description of this lattice leads to an intuitive self-contained exposition of some of the basic facts concerning these orbits, including their enumeration. Given a partition $\\lambda$, the lattice parametrizing orbits in a finite abelian p-group of type $\\lambda$ is found to be independent of p. The order of the orbit corresponding to each parameter, which turns out to be a polynomial in p, is calculated. The description of orbits is extended to subquotients by certain characteristic subgroups. Each such characteristic subquotient is shown to have a unique maximal orbit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-28T06:22:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20K01",
      "05A15"
    ],
    "keywords": [
      "finite abelian group",
      "degeneration",
      "unique maximal orbit",
      "full automorphism group",
      "finite abelian p-group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.5222D"
    }
  }
}