{
  "id": "2109.06693",
  "version": "v1",
  "published": "2021-09-14T13:53:10.000Z",
  "updated": "2021-09-14T13:53:10.000Z",
  "title": "On the realization of subgroups of $PGL(2,F)$, and their automorphism groups, as Galois groups over function fields",
  "authors": [
    "Rod Gow",
    "Gary McGuire"
  ],
  "categories": [
    "math.NT",
    "math.AG",
    "math.GR"
  ],
  "abstract": "Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to realize the automorphism groups of finite subgroups of $PGL(2,F)$ as Galois groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-14T13:53:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12F12",
      "11S20"
    ],
    "keywords": [
      "galois group",
      "function field",
      "automorphism groups",
      "finite subgroup",
      "realization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}