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arXiv · 2001.06221

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

Gareth Tracey·Gunnar Traustason
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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.

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Gareth Tracey, Gunnar Traustason. 2020-01-17. Left $3$-Engel elements in groups of exponent $60$. https://arxiv.org/abs/2001.06221

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