• Title of article

    A NOTE ON ENGEL ELEMENTS IN THE FIRST GRIGORCHUK GROUP

  • Author/Authors

    NOCE, MARIALAURA Department of Mathematics (University of Salerno), Italy , TORTORA, ANTONIO Dipartimento di Matematica - Università di Salerno - Italy

  • Pages
    6
  • From page
    9
  • To page
    14
  • Abstract
    Abstract. Let Γ be the rst Grigorchuk group. According to a result of Bartholdi, the only left Engel elements of Γ are the involutions. This implies that the set of left Engel elements of Γ is not a subgroup. The natural question arises whether this is also the case for the sets of bounded left Engel elements, right Engel elements and bounded right Engel elements of Γ. Motivated by this, we prove that these three subsets of Γ coincide with the identity subgroup.
  • Keywords
    Grigorchuk group , Engel elements
  • Serial Year
    2019
  • Record number

    2493404

    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=10&DC=2493404