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 of a group is a set such that for every all sufficiently long commutators belong to . (Thus, is an Engel element precisely when we can choose .) It is proved that if every element of a compact (Hausdorff) group has a countable (or finite) Engel sink, then has a finite normal subgroup such that is locally nilpotent. This settles a question suggested by J. S. Wilson.

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