{
  "id": "1301.3998",
  "version": "v1",
  "published": "2013-01-17T07:25:26.000Z",
  "updated": "2013-01-17T07:25:26.000Z",
  "title": "Action of dihedral groups",
  "authors": [
    "Ming-chang Kang"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $K$ be any field and $G$ be a finite group. Let $G$ act on the rational function field $K(x_g: \\ g \\in G)$ by $K$-automorphisms defined by $g \\cdot x_h=x_{gh}$ for any $g, \\ h \\in G$. Denote by $K(G)$ the fixed field $K(x_g: \\ g \\in G)^G$. Noether's problem asks whether $K(G)$ is rational (=purely transcendental) over $K$. We will give a brief survey of Noether's problem for abelian groups and dihedral groups, and will show that $\\Bbb Q(D_n)$ is rational over $\\Bbb Q$ for $n \\le 10$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-17T07:25:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E08",
      "13A50",
      "12F12"
    ],
    "keywords": [
      "dihedral groups",
      "rational function field",
      "noethers problem asks",
      "finite group",
      "abelian groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.3998K"
    }
  }
}