Charlotte Scott Centre for Algebra

The paper by **Evgeny Khukhro and Pavel Shumyatsky** **“Almost Engel compact groups”***, *http://dx.doi.org/10.1016/j.jalgebra.2017.04.021, has just been accepted for publication in** Journal of Algebra.**

*Abstract*: We say that a group $latex G$ is almost Engel if for every $latex gin G$ there is a finite set $latex {mathscr E}(g)$ such that for every $latex xin G$ all sufficiently long commutators $latex […[[x,g],g],dots ,g]$ belong to $latex {mathscr E}(g)$, that is, for every $latex xin G$ there is a positive integer $latex n(x,g)$ such that $latex […[[x,g],g],dots ,g]in {mathscr E}(g)$ if $latex g$ is repeated at least $latex n(x,g)$ times. (Thus, Engel groups are precisely the almost Engel groups for which we can choose $latex {mathscr E}(g)={ 1}$ for all $gin G$.) We prove that if a compact (Hausdorff) group $latex G$ is almost Engel, then $latex G$ has a finite normal subgroup $latex N$ such that $latex G/N$ is locally nilpotent…

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