{
  "id": "math/0604337",
  "version": "v1",
  "published": "2006-04-14T14:26:33.000Z",
  "updated": "2006-04-14T14:26:33.000Z",
  "title": "Orders of elements and zeros and heights of characters in a finite group",
  "authors": [
    "Tom Wilde"
  ],
  "comment": "12 pages. Comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let \\chi be an irreducible character of the finite group G. If g is an element of G and \\chi(g) is not zero, then we conjecture that the order of g divides |G|/\\chi(1). The conjecture is a generalization of the classical fact that irreducible p-projective characters vanish on p-singular elements, since the latter is equivalent to saying that if \\chi(g) is not zero then the square free part of the order of g divides |G|/\\chi(1). We prove some partial results on the conjecture; in particular, we show that the order of g divides (|G|/\\chi(1))^2. Using these results, we derive some bounds on heights of characters. We also pose a related conjecture concerning congruences satisfied by central character values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-14T14:26:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C15",
      "20C20"
    ],
    "keywords": [
      "finite group",
      "central character values",
      "square free part",
      "related conjecture concerning congruences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4337W"
    }
  }
}