{
  "id": "2005.12512",
  "version": "v1",
  "published": "2020-05-26T04:47:28.000Z",
  "updated": "2020-05-26T04:47:28.000Z",
  "title": "On the exponents of class groups of some families of imaginary quadratic fields",
  "authors": [
    "Azizul Hoque"
  ],
  "comment": "12 pages. Comments are welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $a\\geq 1$ and $n>1$ be odd integers. For a given prime $p$, we prove under certain conditions that the class groups of imaginary quadratic fields $\\mathbb{Q}(\\sqrt{a^2-4p^n})$ have a subgroup isomorphic to $\\mathbb{Z}/n\\mathbb{Z}$. We also show that this family of fields has infinitely many members with the property that their class groups have a subgroup isomorphic to $\\mathbb{Z}/n\\mathbb{Z}$. In addition, we deduce some unconditional results concerning the divisibility of the class numbers of certain imaginary quadratic fields. At the end, we provide some numerical examples to verify our results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-26T04:47:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R11"
    ],
    "keywords": [
      "imaginary quadratic fields",
      "class groups",
      "subgroup isomorphic",
      "odd integers",
      "unconditional results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}