In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups; they share many properties with their finite quotients.
Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space. Equivalently, one can define a profinite group to be a topological group that is isomorphic to the inverse limit of an inverse...
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