{
  "id": "2311.02784",
  "version": "v1",
  "published": "2023-11-05T22:25:32.000Z",
  "updated": "2023-11-05T22:25:32.000Z",
  "title": "An algorithm to recognize echelon subgroups of a free group",
  "authors": [
    "Dario Ascari"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.GR"
  ],
  "abstract": "We provide an algorithm that, given a finite set of generators for a subgroup $H$ of a finitely generated free group $F$, determines whether $H$ is echelon or not and, in case of affirmative answer, also computes a basis with respect to which $H$ is in echelon form. This answers to a question of A. Rosenmann. We also prove, by means of a counterexample, that intersection of two echelon subgroups needs not to be echelon, answering to another question of A. Rosenmann.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-05T22:25:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E05",
      "20E07",
      "20F65"
    ],
    "keywords": [
      "recognize echelon subgroups",
      "echelon subgroups needs",
      "finitely generated free group",
      "echelon form",
      "finite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}