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.**

(See also https://arxiv.org/pdf/1610.02079.pdf.)

*Abstract*: We say that a group is almost Engel if for every there is a finite set such that for every all sufficiently long commutators belong to , that is, for every there is a positive integer such that if is repeated at least times. (Thus, Engel groups are precisely the almost Engel groups for which we can choose for all $g\in G$.) We prove that if a compact (Hausdorff) group is almost Engel, then has a finite normal subgroup such that is locally nilpotent. If in addition there is a unform bound for the orders of the corresponding sets, then the subgroup can be chosen of order bounded in terms of . The proofs use the Wilson–Zelmanov theorem saying that Engel profinite groups are locally nilpotent.

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