Tags: #todo #todo/stub Refs: ?
profinite group
A profinite group is a topological group that is isomorphic to the inverse limit of discrete finite groups.[
Examples:
- The p-adic integers
- The profinite integers
Profinite completions
Given \(G\in {\mathsf{Grp}}\) a related profinite group \(\widehat{G} \in {\mathsf{Grp}}\), the profinite completion of G. It is defined as \begin{align*} \widehat{G} := \varprojlim_{\substack{ N{~\trianglelefteq~}G \\ [G:N] < \infty }} G/N ,\end{align*} where \(N\) runs through the normal subgroups in G of finite index.
Warning: on computing limits
Examples