A paper accepted by “Proceedings of American Mathematical Society”

A new paper by Cristina Acciarri (Univ. of Brasilia), Evgeny Khukhro (Univ. of Lincoln), and Pavel Shumyatsky (Univ. of Brasilia) “Profinite groups with an automorphism whose fixed points are right Engel” has been accepted for publication in Proceedings of American Mathematical Society. The results of this paper were partially obtained during Evgeny Khukhro’s research visit to University of Brasilia in July of 2018 (supported by a grant of CNPq-Brazil).

Abstract: An element $g$ of a group $G$ is said to be right Engel if for every $x\in G$ there is a number $n=n(g,x)$ such that $[g,{}_{n}x]=1$ . We prove that if a profinite group $G$ admits a coprime automorphism $\varphi$ of prime order such that every fixed point of $\varphi$ is a right Engel element, then $G$ is locally nilpotent.