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Compact groups in which all elements have countable right Engel sinks
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 6 / December 2021
- Published online by Cambridge University Press:
- 13 November 2020, pp. 1790-1814
- Print publication:
- December 2021
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- Article
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A right Engel sink of an element g of a group G is a set
${\mathscr R}(g)$ such that for every x ∈ 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.
