Profinite groups with an automorphism whose fixed points are right Engel

Acciarri, C.; Khukhro, E.; Shumyatsky, P.

doi:10.1090/proc/14519

Profinite groups with an automorphism whose fixed points are right Engel
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by C. Acciarri, E. I. Khukhro and P. Shumyatsky PDF

Proc. Amer. Math. Soc. 147 (2019), 3691-3703 Request permission

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.

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