A note on Engel elements in the first Grigorchuk group
Abstract
Let $\Gamma$ be the first Grigorchuk group. According to a result of Bartholdi, 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. Of particular interest is to wonder whether this happens also 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.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1802.09032
 Bibcode:
 2018arXiv180209032N
 Keywords:

 Mathematics  Group Theory;
 20F45;
 20E08