{
  "id": "0911.0445",
  "version": "v1",
  "published": "2009-11-02T21:41:42.000Z",
  "updated": "2009-11-02T21:41:42.000Z",
  "title": "Groups that together with any transformation generate regular semigroups or idempotent generated semigroups",
  "authors": [
    "Joao Araujo",
    "J. D. Mitchell",
    "Csaba Schneider"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $a$ be a non-invertible transformation of a finite set and let $G$ be a group of permutations on that same set. Then $\\genset{G, a}\\setminus G$ is a subsemigroup, consisting of all non-invertible transformations, in the semigroup generated by $G$ and $a$. Likewise, the conjugates $a^g=g^{-1}ag$ of $a$ by elements $g\\in G$ generate a semigroup denoted $\\genset{a^g | g\\in G}$. We classify the finite permutation groups $G$ on a finite set $X$ such that the semigroups $\\genset{G,a}$, $\\genset{G, a}\\setminus G$, and $\\genset{a^g | g\\in G}$ are regular for all transformations of $X$. We also classify the permutation groups $G$ on a finite set $X$ such that the semigroups $\\genset{G, a}\\setminus G$ and $\\genset{a^g | g\\in G}$ are generated by their idempotents for all non-invertible transformations of $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-02T21:41:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M20",
      "20M17",
      "20B30",
      "20B35",
      "20B15",
      "20B40"
    ],
    "keywords": [
      "transformation generate regular semigroups",
      "idempotent generated semigroups",
      "finite set",
      "non-invertible transformation",
      "finite permutation groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.0445A"
    }
  }
}