{
  "id": "math/0510151",
  "version": "v3",
  "published": "2005-10-07T18:28:59.000Z",
  "updated": "2006-09-19T18:07:46.000Z",
  "title": "Retracts of vertex sets of trees and the almost stability theorem",
  "authors": [
    "Warren Dicks",
    "M. J. Dunwoody"
  ],
  "comment": "15 pages, 0 figures. Formerly titled \"Some refinements of the almost stability theorem\". Version 3",
  "journal": "J. Group Theory 10 (2007), 703-721.",
  "doi": "10.1515/JGT.2007.051",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose vertex set is V'. This fact leads to various new consequences of the almost stability theorem. We also give an example of a group G, a G-tree T and a G-retract V' of VT such that no G-tree has vertex set V'.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-09-19T18:07:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E08",
      "05C25",
      "20J05"
    ],
    "keywords": [
      "vertex set",
      "stability theorem",
      "finite edge stabilizers",
      "vt denote",
      "g-set vt"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10151D"
    }
  }
}