{
  "id": "0808.2753",
  "version": "v4",
  "published": "2008-08-20T14:54:39.000Z",
  "updated": "2011-04-13T13:26:22.000Z",
  "title": "Exterior algebras and two conjectures on finite abelian groups",
  "authors": [
    "Tao Feng",
    "Zhi-Wei Sun",
    "Qing Xiang"
  ],
  "comment": "10 pages",
  "journal": "Israel J. Math. 182(2011), 425-437",
  "categories": [
    "math.GR",
    "math.CO",
    "math.NT"
  ],
  "abstract": "Let G be a finite abelian group with |G|>1. Let a_1,...,a_k be k distinct elements of G and let b_1,...,b_k be (not necessarily distinct) elements of G, where k is a positive integer smaller than the least prime divisor of |G|. We show that there is a permutation $\\pi$ on {1,...,k} such that a_1b_{\\pi(1)},...,a_kb_{\\pi(k)} are distinct, provided that any other prime divisor of |G| (if there is any) is greater than k!. This in particular confirms the Dasgupta-Karolyi-Serra-Szegedy conjecture for abelian p-groups. We also pose a new conjecture involving determinants and characters, and show that its validity implies Snevily's conjecture for abelian groups of odd order. Our methods involve exterior algebras and characters.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2011-04-13T13:26:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D60",
      "05A05",
      "05E99",
      "11B75",
      "11P99",
      "15A75",
      "20K01"
    ],
    "keywords": [
      "finite abelian group",
      "exterior algebras",
      "validity implies snevilys conjecture",
      "prime divisor",
      "characters"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.2753F"
    }
  }
}