University of IsfahanInternational Journal of Group Theory2251-76508320190901A note on Engel elements in the first Grigorchuk group9142272510.22108/ijgt.2018.109911.1470ENMarialaura NoceDepartment of Mathematics (University of Salerno), Italy - Department of Mathematics and Statistic (University of the Basque Country), SpainAntonio TortoraDipartimento di Matematica,
Università di Salerno - ItalyJournal Article20180225Let $Gamma$ be the first Grigorchuk group. According to a result of Bar-thol-di, the only left Engel elements of $Gamma$ are the involutions. This implies that the set of left Engel elements of $Gamma$ 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 $Gamma$. Motivated by this, we prove that these three subsets of $Gamma$ coincide with the identity subgroup.http://ijgt.ui.ac.ir/article_22725_55618dd0d66c94f763a4a6c2edb40de4.pdf