Let Γ be the first Grigorchuk group‎. ‎According to a result of Bar-thol-di‎, ‎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.

A note on Engel elements in the first Grigorchuk group

Noce M.;Tortora A.
2019

Abstract

Let Γ be the first Grigorchuk group‎. ‎According to a result of Bar-thol-di‎, ‎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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4726087
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