Left $3$-Engel elements in groups of exponent $60$

Gareth Tracey; Gunnar Traustason

Left $3$-Engel elements in groups of exponent $60$

Group Theory 2020-01-20 v1

Authors: Gareth Tracey , Gunnar Traustason

Abstract

Let $G$ be a group and let $x\in G$ be a left $3$ -Engel element of order dividing $60$ . Suppose furthermore that $\langle x\rangle^{G}$ has no elements of order $8$ , $9$ and $25$ . We show that $x$ is then contained in the locally nilpotent radical of $G$ . In particular all the left $3$ -Engel elements of a group of exponent $60$ are contained in the locally nilpotent radical.

Cite

@article{arxiv.2001.06221,
  title  = {Left $3$-Engel elements in groups of exponent $60$},
  author = {Gareth Tracey and Gunnar Traustason},
  journal= {arXiv preprint arXiv:2001.06221},
  year   = {2020}
}

Comments

This is a belated post of a 2018 paper

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