{
  "id": "2405.18409",
  "version": "v1",
  "published": "2024-05-28T17:51:04.000Z",
  "updated": "2024-05-28T17:51:04.000Z",
  "title": "Sections of Submonoids of Nilpotent Groups",
  "authors": [
    "Doron Shafrir"
  ],
  "categories": [
    "math.GR",
    "cs.FL"
  ],
  "abstract": "We show that every product of f.g.\\ submonoids of a group $G$ is a section of a f.g.\\ submonoid of $G{\\times}H_5(\\mathbb{Z})$, where $H_5(\\mathbb{Z})$ is a Heisenberg group. This gives us a converse of a reduction of Bodart, and a new simple proof of the existence of a submonoid of a nilpotent group of class 2 with undecidable membership problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-28T17:51:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nilpotent group",
      "heisenberg group",
      "simple proof",
      "undecidable membership problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}