Khukhro, Evgeny and Shumyatsky, Pavel (2020) Compact groups in which all elements have countable right Engel sinks. Proceedings of the Royal Society of Edinburgh Section A: Mathematics . ISSN 0308-2105
Full content URL: https://doi.org/10.1017/prm.2020.81
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| Item Type: | Article |
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| Item Status: | Live Archive |
Abstract
A right Engel sink of an element $g$ of a group $G$ is a set ${\mathscr R}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[g,x],x],\dots ,x]$ belong to ${\mathscr R}(g)$. (Thus, $g$ is a right Engel element precisely when we can choose ${\mathscr R}(g)=\{ 1\}$.) It is proved that if every element of a compact (Hausdorff) group $G$ has a countable right Engel sink, then $G$ has a finite normal subgroup $N$ such that $G/N$ is locally nilpotent.
| Keywords: | Compact groups, profinite groups, pro-$p$ groups, finite groups, Lie ring method, Engel condition, locally nilpotent groups |
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| Subjects: | G Mathematical and Computer Sciences > G110 Pure Mathematics |
| Divisions: | College of Science > School of Mathematics and Physics |
| ID Code: | 43362 |
| Deposited On: | 15 Dec 2020 12:05 |
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Compact groups in which all elements have countable right Engel sinks. (deposited 17 Nov 2020 12:03)
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