New paper accepted in Journal of Algebra

The paper JA-coverby 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 G is almost Engel if for every g\in G there is a finite set {\mathscr E}(g) such that for every x\in G all sufficiently long commutators [...[[x,g],g],\dots ,g] belong to {\mathscr E}(g), that is, for every  x\in G there is a positive integer n(x,g) such that [...[[x,g],g],\dots ,g]\in {\mathscr E}(g) if g is repeated at least n(x,g) times. (Thus, Engel groups are precisely the almost Engel groups for which we can choose {\mathscr E}(g)=\{ 1\} for all $g\in G$.) We prove that if a compact (Hausdorff) group G is almost Engel, then G has a finite normal subgroup N such that G/N is locally nilpotent. If in addition there is a unform bound |{\mathscr E}(g)|\leq m for the orders of the corresponding sets, then the subgroup N can be chosen of order bounded in terms of m. The proofs use the Wilson–Zelmanov theorem saying that Engel profinite groups are locally nilpotent.

 

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One Comment

  1. Posted May 5, 2017 at 13:33 | Permalink | Reply

    Reblogged this on Maths & Physics News.

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