Charlotte Scott Centre for Algebra

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 $latex g$ of a group $latex G$ is a set $latex {mathscr E}(g)$ such that for every $latex xin G$ all sufficiently long commutators $latex […[[x,g],g],dots ,g]$ belong to $latex {mathscr E}(g)$. (Thus, $latex g$ is an Engel element precisely when we can choose $latex {mathscr E}(g)={ 1}$.) It is proved that if every element of a compact (Hausdorff) group $latex G$ has a countable (or finite) Engel sink, then $latex G$ has a finite normal subgroup $latex N$ such…

View original post 15 more words

## Leave a Reply