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arXiv · 1802.09032

A note on Engel elements in the first Grigorchuk group

Marialaura Noce·Antonio Tortora
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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.

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Marialaura Noce, Antonio Tortora. 2018-02-25. A note on Engel elements in the first Grigorchuk group. https://arxiv.org/abs/1802.09032

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