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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 aprofinite group $G$ admits a coprime automorphism $\varphi$ of prime order suchthat every fixed point of $\varphi$ is a right Engel element, then $G$ islocally nilpotent.

Profinite groups with an automorphism whose fixed points are right Engel