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 of a group , an Engel sink is a subset such that for every all sufficiently long commutators belong to . A finite group is nilpotent if and only if every element has a trivial Engel sink. We prove that if in a finite group every element has an Engel sink generating a subgroup of rank , then has a normal subgroup of rank bounded in terms of such that is nilpotent.

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