A note on Engel elements in the first Grigorchuk group
عنوان مقاله: A note on Engel elements in the first Grigorchuk group
شناسه ملی مقاله: JR_THEGR-8-3_002
منتشر شده در در سال 1398
شناسه ملی مقاله: JR_THEGR-8-3_002
منتشر شده در در سال 1398
مشخصات نویسندگان مقاله:
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
خلاصه مقاله:
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
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.
کلمات کلیدی: Engel elements, Grigorchuk group
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1194948/