Year: 2020
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Tracey, Gareth, Traustason, Gunnar
Institution: University of Bath
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2998910583