{
  "id": "2502.03215",
  "version": "v1",
  "published": "2025-02-05T14:30:17.000Z",
  "updated": "2025-02-05T14:30:17.000Z",
  "title": "Subgroups of Bestvina-Brady groups",
  "authors": [
    "Simone Blumer"
  ],
  "categories": [
    "math.GR",
    "math.CO",
    "math.RA"
  ],
  "abstract": "In \"Subgroups of Graph Groups\", 1987, J. Alg., Droms proved that all the subgroups of a right-angled Artin group (RAAG) defined by a finite simplicial graph $\\Gamma$ are themselves RAAGs if, and only if, $\\Gamma$ has no induced square graph nor line-graph of length $3$. The present work provides a similar result for specific normal subgroups of RAAGs, called Bestvina-Brady groups: We characterize those graphs in which every subgroup of such a group is itself a RAAG. In turn, we confirm several Galois theoretic conjectures for the pro-$p$ completions of these groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-05T14:30:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "05C35",
      "17B56"
    ],
    "keywords": [
      "bestvina-brady groups",
      "finite simplicial graph",
      "specific normal subgroups",
      "galois theoretic conjectures",
      "similar result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}