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Questions about the branch of algebra that deals with groups.

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Linear embeddings of nilpotent pro-$p$ groups

Yes, this is true. In the argument below, all references are to the book Analytic Pro-$p$ Groups by Dixon–Du Sautoy–Mann–Segal. Let $G$ be a finitely generated torsion-free nilpotent pro-$p$ group. We …
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