{
  "id": "2202.08169",
  "version": "v1",
  "published": "2022-02-16T16:16:14.000Z",
  "updated": "2022-02-16T16:16:14.000Z",
  "title": "On the virtual and residual properties of a generalization of Bestvina-Brady groups",
  "authors": [
    "Ian J Leary",
    "Vladimir Vankov"
  ],
  "comment": "23 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "Previously one of us introduced a family of groups $G^M_L(S)$, parametrized by a finite flag complex $L$, a regular covering $M$ of $L$, and a set $S$ of integers. We give conjectural descriptions of when $G^M_L(S)$ is either residually finite or virtually torsion-free. In the case that $M$ is a finite cover and $S$ is periodic, there is an extension with kernel $G_L^M(S)$ and infinite cyclic quotient that is a CAT(0) cubical group. We conjecture that this group is virtually special. We relate these three conjectures to each other and prove many cases of them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-16T16:16:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F65",
      "20E26",
      "57M07"
    ],
    "keywords": [
      "bestvina-brady groups",
      "residual properties",
      "generalization",
      "finite flag complex",
      "infinite cyclic quotient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}