{
  "id": "2003.06546",
  "version": "v1",
  "published": "2020-03-14T04:04:11.000Z",
  "updated": "2020-03-14T04:04:11.000Z",
  "title": "On $p$-class groups of relative cyclic $p$-extensions",
  "authors": [
    "Yasushi Mizusawa",
    "Kota Yamamoto"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove a general stability theorem for $p$-class groups of number fields along relative cyclic extensions of degree $p^2$, which is a generalization of a finite-extension version of Fukuda's theorem by Li, Ouyang, Xu and Zhang. As an application, we give an example of pseudo-null Iwasawa module over a certain $2$-adic Lie extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-14T04:04:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R29",
      "11R23"
    ],
    "keywords": [
      "class groups",
      "general stability theorem",
      "pseudo-null iwasawa module",
      "adic lie extension",
      "number fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}