University of Isfahan International Journal of Group Theory 2251-7650 8 3 2019 09 01 A note on Engel elements in the first Grigorchuk group 9 14 22725 10.22108/ijgt.2018.109911.1470 EN Marialaura Noce Department of Mathematics (University of Salerno), Italy - Department of Mathematics and Statistic (University of the Basque Country), Spain Antonio Tortora Dipartimento di Matematica, Università di Salerno - Italy Journal Article 2018 02 25 Let $\Gamma$ 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. https://ijgt.ui.ac.ir/article_22725_55618dd0d66c94f763a4a6c2edb40de4.pdf