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
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
