{
  "id": "1201.1610",
  "version": "v2",
  "published": "2012-01-08T06:00:26.000Z",
  "updated": "2012-09-13T08:52:20.000Z",
  "title": "On finite factors of centralizers of parabolic subgroups in Coxeter groups",
  "authors": [
    "Koji Nuida"
  ],
  "comment": "44 pages, 4 figures, 19 tables, separated from Section 7 of arXiv:math/0501061v4 [math.GR] with improvements; (v2) 43 pages, 5 figures, 16 tables, the size of counterexample is reduced, some parts are slightly revised",
  "journal": "Tsukuba Journal of Mathematics, vol.36, no.2 (2012).235-294",
  "categories": [
    "math.GR"
  ],
  "abstract": "It has been known that the centralizer $Z_W(W_I)$ of a parabolic subgroup $W_I$ of a Coxeter group $W$ is a split extension of a naturally defined reflection subgroup by a subgroup defined by a 2-cell complex $\\mathcal{Y}$. In this paper, we study the structure of $Z_W(W_I)$ further and show that, if $I$ has no irreducible components of type $A_n$ with $2 \\leq n < \\infty$, then every element of finite irreducible components of the inner factor is fixed by a natural action of the fundamental group of $\\mathcal{Y}$. This property has an application to the isomorphism problem in Coxeter groups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-13T08:52:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "20E34"
    ],
    "keywords": [
      "coxeter group",
      "parabolic subgroup",
      "finite factors",
      "centralizer",
      "split extension"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.1610N"
    }
  }
}