{
  "id": "1310.4625",
  "version": "v1",
  "published": "2013-10-17T09:14:33.000Z",
  "updated": "2013-10-17T09:14:33.000Z",
  "title": "Inertial endomorphisms of an abelian group",
  "authors": [
    "Ulderico Dardano",
    "Silvana Rinauro"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We describe inertial endomorphisms of an abelian group $A$, that is endomorphisms $\\varphi$ with the property $|(\\varphi(X)+X)/X|<\\infty$ for each $X\\le A$. They form a ring containing multiplications, the so-called finitary endomorphisms and non-trivial instances. We show that inertial invertible endomorphisms form a group, provided $A$ has finite torsion-free rank. In any case, the group $IAut(A)$ they generate is commutative modulo the group $FAut(A)$ of finitary automorphisms, which is known to be locally finite. We deduce that $IAut(A)$ is locally-(center-by-finite). Also we consider the lattice dual property, that is that $|X/(X\\cap \\varphi(X))|<\\infty$ for each $X\\le A$. We show that this implies the above one, provided $A$ has finite torsion-free rank.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-17T09:14:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian group",
      "inertial endomorphisms",
      "finite torsion-free rank",
      "lattice dual property",
      "inertial invertible endomorphisms form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4625D"
    }
  }
}