Definition:Profinite Group

Definition 1
A profinite group is a topological group that is isomorphic to a small inverse limit of finite discrete groups, with the inverse limit topology.

Definition 2
A profinite group is a topological group that is compact, Hausdorff and totally disconnected.

Also see

 * Equivalence of Definitions of Profinite Group
 * Definition:Category of Profinite Groups