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Questions about the branch of algebra that deals with groups.
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Can finite index be seen at the level of profinite completion
Let $G$ be a group, and $H$ a subgroup of $G$.
Is it possible to "see" from the profinite completions of $H$ and $G$ that $H$ has finite index in $G$?
Naively, does $H$ have finite index in $G$ iff …