Algebra in Lincoln

School of Mathematics & Physics, University of Lincoln

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.

 

One comment on “New paper accepted in Journal of Algebra

  1. Evgeny Khukhro
    May 5, 2017

    Reblogged this on Maths & Physics News.

    Like

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This entry was posted on May 5, 2017 by in New publications, News and announcements.
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