{
  "id": "2206.12631",
  "version": "v1",
  "published": "2022-06-25T12:14:35.000Z",
  "updated": "2022-06-25T12:14:35.000Z",
  "title": "Type systems and maximal subgroups of Thompson's group $V$",
  "authors": [
    "James Belk",
    "Collin Bleak",
    "Martyn Quick",
    "Rachel Skipper"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We introduce the concept of a type system~$\\Part$, that is, a partition on the set of finite words over the alphabet~$\\{0,1\\}$ compatible with the partial action of Thompson's group~$V$, and associate a subgroup~$\\Stab{V}{\\Part}$ of~$V$. We classify the finite simple type systems and show that the stabilizers of various simple type systems, including all finite simple type systems, are maximal subgroups of~$V$. In particular, we show that there are uncountably many maximal subgroups of~$V$ that occur as the stabilizers of simple type systems and do not arise in the form of previously known maximal subgroups. Finally, we consider two conditions for subgroups of~$V$ that could be viewed as related to the concept of primitivity. We show that in fact only $V$~itself satisfies either of these conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-25T12:14:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E28",
      "20E32",
      "20F65"
    ],
    "keywords": [
      "maximal subgroups",
      "finite simple type systems",
      "thompsons group",
      "stabilizers",
      "partial action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}