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16.40 (2006)

Open

Let $\Delta$ be a subgroup of the automorphism group of a free pro-$p$ group of finite rank $F$ such that $\Delta$ is isomorphic (as a profinite group) to the group $\mathbb{Z}_p$ of $p$-adic integers. Is the subgroup of fixed points of $\Delta$ in $F$ finitely generated (as a profinite group)?

Contributor: P. A. Zalesskiĭ

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