{
  "id": "2408.11724",
  "version": "v1",
  "published": "2024-08-21T15:52:25.000Z",
  "updated": "2024-08-21T15:52:25.000Z",
  "title": "On soficity for certain fundamental groups of graphs of groups",
  "authors": [
    "David Gao",
    "Srivatsav Kunnawalkam Elayavalli",
    "Mahan Mj"
  ],
  "categories": [
    "math.GR",
    "math.OA"
  ],
  "abstract": "In this note we study a family of graphs of groups over arbitrary base graphs where all vertex groups are isomorphic to a fixed countable sofic group $G$, and all edge groups $H<G$ are such that the embeddings of $H$ into $G$ are identical everywhere. We prove soficity for this family of groups under a flexible technical hypothesis for $H$ called $\\sigma$-co-sofic. This proves soficity for group doubles $*_H G$, where $H<G$ is an arbitrary separable subgroup and $G$ is countable and sofic. This includes arbitrary finite index group doubles of sofic groups among various other examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-21T15:52:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fundamental groups",
      "arbitrary finite index group doubles",
      "arbitrary base graphs",
      "vertex groups",
      "edge groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}