{
  "id": "2305.16054",
  "version": "v1",
  "published": "2023-05-25T13:37:28.000Z",
  "updated": "2023-05-25T13:37:28.000Z",
  "title": "Profinite genus of free products with finite amalgamation",
  "authors": [
    "Vagner R. de Bessa",
    "Anderson L. P. Porto",
    "Pavel A. Zalesskii"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "A finitely generated residually finite group $G$ is an $\\widehat{OE}$-group if any action of its profinite completion $\\widehat G$ on a profinite tree with finite edge stabilizers admits a global fixed point. In this paper, we study the profinite genus of free products $G_1*_HG_2$ of $\\widehat{OE}$-groups $G_1,G_2$ with finite amalgamation $H$. Given such $G_1,G_2,H$ we give precise formulas for the number of isomorphism classes of $G_1*_HG_2$ and of its profinite completion. We compute the genus of $G_1*_HG_2$ and list various situations when the formula for the genus simplifies.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-25T13:37:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "profinite genus",
      "free products",
      "finite amalgamation",
      "generated residually finite group",
      "finite edge stabilizers admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}