New paper accepted by Monatshefte für Mathematik

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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