{
  "id": "math/0402389",
  "version": "v1",
  "published": "2004-02-24T13:01:35.000Z",
  "updated": "2004-02-24T13:01:35.000Z",
  "title": "Parabolic subgroups of Garside groups",
  "authors": [
    "Eddy Godelle"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion of a Garside subgroup of a Garside group, which is related to the notion of LCM-homomorphisms between Artin-Tits groups. We prove that most of the properties of parabolic subgroups extend to this subgroups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-02-24T13:01:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36"
    ],
    "keywords": [
      "artin-tits group",
      "garside monoid",
      "finite lattice generating set",
      "garside groups contains",
      "parabolic subgroups extend"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......2389G"
    }
  }
}