{
  "id": "1801.03229",
  "version": "v1",
  "published": "2018-01-10T03:36:40.000Z",
  "updated": "2018-01-10T03:36:40.000Z",
  "title": "A proof of some conjecture about fixed points of automorphisms of $\\mathbf{Z}_{p} \\oplus \\mathbf{Z}_{p^2}$",
  "authors": [
    "Daniel López-Aguayo"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $G=\\mathbf{Z}_{p} \\oplus \\mathbf{Z}_{p^2}$ where $p$ is a prime number. Suppose that $d$ is a divisor of $G$. In this paper we find the number of automorphisms of $G$ fixing $d$ elements of $G$, and denote it by $\\theta(G,d)$. As a consequence, we prove Conjecture $1$ of [2].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-10T03:36:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fixed points",
      "automorphisms",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}