New paper by **Evgeny Khukhro (Univ. of Lincoln) and Pavel Shumyatsky (Univ. of Brasilia)** “Profinite groups with an automorphism of prime order whose fixed points have finite Engel sinks” has been accepted for publication in the *Monatshefte für Mathematik*. The work was supported by FAPDF and CNPq-Brazil, and stems from the collaboration with University of Brasilia.

*Abstract*: A right Engel sink of an element of a group is a set such that for every all sufficiently long commutators belong to . (Thus, is a right Engel element precisely when we can choose .) We prove that if a profinite group admits a coprime automorphism of prime order such that every fixed point of has a finite right Engel sink, then has an open locally nilpotent subgroup.

A left Engel sink of an element of a group is a set such that for every all sufficiently long commutators belong to . (Thus, is a left Engel element precisely when we can choose .) We prove that if a profinite group admits a coprime automorphism of prime order such that every fixed point of has a finite left Engel sink, then has an open pronilpotent-by-nilpotent subgroup.

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