School of Mathematics & Physics, University of Lincoln
New paper by Evgeny Khukhro (Univ. of Lincoln) and Pavel Shumyatsky (Univ. of Brasilia) “On profinite groups with automorphisms whose fixed points have countable Engel sinkss” has been accepted for publication in the Israel Journal of Mathematics. The work was supported by Mathematical Center in Akademgorodok, FAPDF and CNPq-Brazil, and stems from the collaboration with University of Brasilia.
Abstract: An Engel sink of an element of a group is a set such that for every all sufficiently long commutators belong to . (Thus, is an Engel element precisely when we can choose .) It is proved that if a profinite group admits an elementary abelian group of automorphisms of coprime order for a prime such that for each every element of the centralizer has a countable (or finite) Engel sink, then has a finite normal subgroup such that is locally nilpotent.