Definition:Profinite Group

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Definition

Let $\struct {G, \odot, \tau}$ be a topological group.


Definition 1

$\struct {G, \odot, \tau}$ is profinite if and only if it is isomorphic in the category of topological groups to a small inverse limit of finite discrete groups, with the limit topology.


Definition 2

$\struct {G, \odot, \tau}$ is profinite if and only if it is compact, Hausdorff and totally disconnected.


Also see

  • Results about profinite groups can be found here.


Sources