{
  "id": "math/0504401",
  "version": "v2",
  "published": "2005-04-20T04:46:45.000Z",
  "updated": "2005-04-26T00:48:22.000Z",
  "title": "Algorithmic constructions and primitive elements in the free group of rank 2",
  "authors": [
    "Adam Piggott"
  ],
  "comment": "12 pages. Replaces old version (apologies for uploading wrong version) which contained an error in the statement of Second normal form theorem",
  "categories": [
    "math.GR"
  ],
  "abstract": "The centrepiece of this paper is a normal form for primitive elements which facilitates the use of induction arguments to prove properties of primitive elements. The normal form arises from an elementary algorithm for constructing a primitive element p in F(x, y) with a given exponent sum pair (X, Y), if such an element p exists. Several results concerning the primitive elements of F(x, y) are recast as applications of the algorithm and the normal form.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-04-26T00:48:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05"
    ],
    "keywords": [
      "primitive element",
      "free group",
      "algorithmic constructions",
      "normal form arises",
      "exponent sum pair"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4401P"
    }
  }
}