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21.9 (2026)

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Let $F$ be a non-abelian free pro-$p$ group of finite rank. Can one find a finite collection $U_1, \dots, U_n$ of open subgroups of $F$ including $F$ itself such that the only subgroup of $F$ which is contained in $U_i$ and is characteristic in $U_i$ for every $i$ is the trivial subgroup?

Contributor: Y. Barnea

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