{
  "id": "1902.03822",
  "version": "v1",
  "published": "2019-02-11T11:25:44.000Z",
  "updated": "2019-02-11T11:25:44.000Z",
  "title": "Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups",
  "authors": [
    "Robert D. Gray"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We prove the following results: (1) There is a one-relator inverse monoid $\\mathrm{Inv}\\langle A\\:|\\:w=1 \\rangle$ with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The first of these results answers a problem originally posed by Margolis, Meakin and Stephen in 1987.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-11T11:25:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F10",
      "20F05",
      "20M05",
      "20M18",
      "20F36"
    ],
    "keywords": [
      "one-relator inverse monoid",
      "right-angled artin subgroups",
      "one-relator groups",
      "undecidability",
      "undecidable submonoid membership problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}