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An open subgroup $H$ of a profinite group $G$ is a subgroup that is open in the topology of $G$, which implies that it is equal to the inverse image of its projection to a a finite quotient of $G$.

Open subgroups of $G$ necessarily have finite index (since $G$ is compact), but not every finite index subgroup of $G$ is necessarily open.

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• Review status: beta
• Last edited by Andrew Sutherland on 2021-07-17 14:56:54
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