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It is well known that every subgroup $H$ of a finite abelian group $G$ is isomorphic to a quotient of $G$. I'm wondering whether there is a counterpart for profinite groups. For example is it true ...

Let $d,n \in \mathbb{N}$, and $p$ a prime number. Let $F$ be a free pro-$p$ group on $d$ generators. Is there an automorphism of $F$ of order $n$?