Compact groups in which all elements have countable right Engel sinks

Abstract

A right Engel sink of an element $g$ of a group $G$ is a set $\mathcal{R}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[g,x],x],\dots ,x]$ belong to $\mathcal{R}(g)$. (Thus, $g$ is a right Engel element precisely when we can choose $\mathcal{R}(g)=\{1\}$.) It is proved that if every element of a compact (Hausdorff) group $G$ has a countable (or finite) right Engel sink, then $G$ has a finite normal subgroup $N$ such that $G/N$ is locally nilpotent.

arXiv admin note: text overlap with arXiv:1908.11637