{
  "id": "1007.0541",
  "version": "v1",
  "published": "2010-07-04T11:35:39.000Z",
  "updated": "2010-07-04T11:35:39.000Z",
  "title": "Algebraic entropy of shift endomorphisms on abelian groups",
  "authors": [
    "Maryam Akhavin",
    "Fatemah Ayatollah Zadeh Shirazi",
    "Dikran Dikranjan",
    "Anna Giordano Bruno",
    "Arezoo Hosseini"
  ],
  "comment": "15 pages",
  "journal": "Quaest. Math. 32 (2009) no. 4, 529-550",
  "categories": [
    "math.GR"
  ],
  "abstract": "For every finite-to-one map $\\lambda:\\Gamma\\to\\Gamma$ and for every abelian group $K$, the generalized shift $\\sigma_\\lambda$ of the direct sum $\\bigoplus_\\Gamma K$ is the endomorphism defined by $(x_i)_{i\\in\\Gamma}\\mapsto(x_{\\lambda(i)})_{i\\in\\Gamma}$. In this paper we analyze and compute the algebraic entropy of a generalized shift, which turns out to depend on the cardinality of $K$, but mainly on the function $\\lambda$. We give many examples showing that the generalized shifts provide a very useful universal tool for producing counter-examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-04T11:35:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian group",
      "algebraic entropy",
      "shift endomorphisms",
      "generalized shift",
      "direct sum"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.0541A"
    }
  }
}