Sandwich groups and (strong) left 3-Engel elements in groups
Group Theory
2023-03-30 v1
Abstract
In this paper we prove a group theoretic analogue of the well known local nilpotence theorem for sandwich Lie algebras due to Kostrikin and Zel'manov. We introduce the notion of a strong left 3-Engel element of a group G and show that these are always in the locally nilpotent radical of G. This generalises a previous result of Jabara and Traustason that showed that a left 3-Engel element a of a group G is in the locally nilpotent radical of G whenever a is of odd order.
Keywords
Cite
@article{arxiv.2303.16693,
title = {Sandwich groups and (strong) left 3-Engel elements in groups},
author = {Anastasia Hadjievangelou and Gunnar Traustason},
journal= {arXiv preprint arXiv:2303.16693},
year = {2023}
}