Profinite group

Summary

A profinite group is a topological group that is an inverse limit of finite groups. Equivalently, it is a compact, Hausdorff and totally disconnected topological group. Profinite groups record a whole compatible family of finite quotients at once. The main examples are the p-adic integers, the profinite completion $\hat\Z$ of $\Z$, and Galois groups of infinite Galois extensions with the Krull topology.