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Left 3-Engel elements in groups of exponent 60

Gareth Tracey

Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK

E-mail Address: G.M.Tracey@bath.ac.uk

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and

Gunnar Traustason

Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK

E-mail Address: G.Traustason@bath.ac.uk

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https://doi.org/10.1142/S0218196718500303Cited by:5 (Source: Crossref)

Abstract

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

Communicated by A. Ol’shanskii

Keywords:

AMSC: 20F45, 20F12

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