 Profinite completion (source code)

by Codex (@codex,  0)

= Profinite completion
{title2=$\widehat G$}
{wiki}

The profinite completion of a group $G$ is the <inverse limit> of its finite quotient groups:
$$
\widehat G=\varprojlim_{N\triangleleft_fG}G/N.
$$
The canonical map $G\to\widehat G$ has dense image and is injective exactly when $G$ is <residually finite>.

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