# Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

# New result of collaboration of mathematicians of Lincoln and Brasilia

During 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.

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