{
  "id": "2502.03626",
  "version": "v1",
  "published": "2025-02-05T21:24:55.000Z",
  "updated": "2025-02-05T21:24:55.000Z",
  "title": "Cyclic splittings of pro-$\\mathcal{C}$ groups",
  "authors": [
    "Jesus Berdugo",
    "Pavel Zalesskii"
  ],
  "categories": [
    "math.GR",
    "math.AG"
  ],
  "abstract": "In this paper we proved a pro-$\\mathcal{C}$ version of the Rips-Sela Theorems on splittings as an amalgamated free product or HNN-extension over a cyclic subgroup, where $\\mathcal{C}$ is a class of finite groups closed for subgroups, quotients, finite direct products and extensions with abelian kernel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-05T21:24:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic splittings",
      "finite direct products",
      "abelian kernel",
      "rips-sela theorems",
      "finite groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}