{
  "id": "2102.03477",
  "version": "v1",
  "published": "2021-02-06T02:27:23.000Z",
  "updated": "2021-02-06T02:27:23.000Z",
  "title": "The classification problem for extensions of torsion abelian groups",
  "authors": [
    "Martino Lupini"
  ],
  "comment": "37 pages",
  "categories": [
    "math.GR",
    "math.AC",
    "math.LO"
  ],
  "abstract": "Given countable abelian groups $C,A$, with $C$ torsion, we compute the potential complexity class of the classification problem for extensions of $C$ by $A$. In particular, we show that such a problem can have arbitrarily high potential complexity. Toward this goal, we further develop the theory of groups with a Polish cover, in particular by showing that they form an abelian category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-06T02:27:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20K10",
      "20K35",
      "54H05",
      "20K40",
      "20K45"
    ],
    "keywords": [
      "torsion abelian groups",
      "classification problem",
      "extensions",
      "potential complexity class",
      "arbitrarily high potential complexity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}