New paper of a Lincoln algebraist in a high-ranking mathematical journal

New paper by Evgeny Khukhro (Univ. of Lincoln) and Pavel Shumyatsky (Univ. of Brasilia) “Compact groups with countable Engel sinks” has been accepted for publication in one of the highest-ranking mathematical journals Bulletin of Mathematical Sciences. The work was supported by Mathematical Center in Akademgorodok, FAPDF and CNPq-Brazil, and stems from the collaboration with University of Brasilia.

Abstract: An Engel sink of an element $g$ of a group $G$ is a set ${\mathscr E}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[x,g],g],\dots ,g]$ belong to ${\mathscr E}(g)$ . (Thus, $g$ is an Engel element precisely when we can choose ${\mathscr E}(g)=\{ 1\}$ .) It is proved that if every element of a compact (Hausdorff) group $G$ has a countable (or finite) Engel sink, then $G$ has a finite normal subgroup $N$ such that $G/N$ is locally nilpotent. This settles a question suggested by J. S. Wilson.