{
  "id": "1804.03695",
  "version": "v1",
  "published": "2018-04-10T19:26:55.000Z",
  "updated": "2018-04-10T19:26:55.000Z",
  "title": "Reidemeister classes in some weakly branch groups",
  "authors": [
    "Evgenij Troitsky"
  ],
  "comment": "9 pages",
  "categories": [
    "math.GR",
    "math.DS"
  ],
  "abstract": "We prove that a saturated weakly branch group $G$ has the property $R_\\infty$ (any automorphism $\\phi:G\\to G$ has infinite Reidemeister number) in each of the following cases: 1) any element of $Out(G)$ has finite order; 2) for any $\\phi$ the number of orbits on levels of the tree automorphism $t$ inducing $\\phi$ is uniformly bounded and $G$ is weakly stabilizer transitive; 3) $G$ is finitely generated, prime-branching, and weakly stabilizer transitive with some non-abelian stabilizers (with no restrictions on automorphisms). Some related facts and generalizations are proved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-10T19:26:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20E45",
      "20B35",
      "20F28",
      "20F65"
    ],
    "keywords": [
      "reidemeister classes",
      "weakly stabilizer transitive",
      "infinite reidemeister number",
      "finite order",
      "tree automorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}