Engel elements in weakly branch groups

Gustavo A. Fernández-Alcober, Marialaura Noce, Gareth M. Tracey

Research output: Contribution to journalArticle

Abstract

We study properties of Engel elements in weakly branch groups, lying in the group of automorphisms of a spherically homogeneous rooted tree. More precisely, we prove that the set of bounded left Engel elements is always trivial in weakly branch groups. In the case of branch groups, the existence of non-trivial left Engel elements implies that these are all p-elements and that the group is virtually a p-group (and so periodic) for some prime p. We also show that the set of right Engel elements of a weakly branch group is trivial under a relatively mild condition. Also, we apply these results to well-known families of weakly branch groups, like the multi-GGS groups.

Original languageEnglish
Pages (from-to)54-77
JournalJournal of Algebra
Volume554
Early online date19 Mar 2020
DOIs
Publication statusPublished - 15 Jul 2020

Keywords

  • Branch groups
  • Engel elements

ASJC Scopus subject areas

  • Algebra and Number Theory

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