Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

New result of collaboration of mathematicians of Lincoln and Brasilia

P1030435aDuring his recent trip to Brazil Evgeny Khukhro completed a new joint paper with Prof Pavel Shumyatsky (Univ. of Brasilia) “Finite groups with Engel sinks of bounded rank” (available on ArXiv).

Abstact: For an element g of a group G, an Engel sink is a subset {\mathscr E}(g) such that for every x\in G all sufficiently long commutators [...[[x,g],g],\dots ,g] belong to {\mathscr E}(g). A finite group is nilpotent if and only if every element has a trivial Engel sink. We prove that if in a finite group G every element has an Engel sink generating a subgroup of rank r, then G has a normal subgroup N of rank bounded in terms of r such that G/N is nilpotent.

One comment on “New result of collaboration of mathematicians of Lincoln and Brasilia

  1. Evgeny Khukhro
    August 23, 2017

    Reblogged this on Maths & Physics News.

    Like

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This entry was posted on August 22, 2017 by in New publications, News and announcements, Recent places, Talks and visits.
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