Charlotte Scott Centre for Algebra

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

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