{
  "id": "2407.09279",
  "version": "v1",
  "published": "2024-07-12T14:11:56.000Z",
  "updated": "2024-07-12T14:11:56.000Z",
  "title": "On groups well represented as automorphism groups of groups",
  "authors": [
    "Mohsen Asgharzadeh",
    "Mohammad Golshani",
    "Daniel Herden",
    "Saharon Shelah"
  ],
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "Assuming G\\\"{o}del's axiom of constructibility $\\bold V=\\bold L,$ we present a characterization of those groups $L$ for which there exist arbitrarily large groups $H$ such that $aut(H) \\cong L$. In particular, we show that it suffices to have one such group $H$ such that the size of its center is bigger than $ 2^{|L |+\\aleph_0}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-12T14:11:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism groups",
      "arbitrarily large groups",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}