School of Mathematics & Physics, University of Lincoln
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.