What is Locally profinite group?

In mathematics, a locally profinite group is a Hausdorff topological group in which every neighborhood of the identity element contains a compact open subgroup. Equivalently, a locally profinite group is a topological group that is Hausdorff, locally compact, and totally disconnected. Moreover, a locally profinite group is compact if and only if it is profinite; this explains the terminology. Basic examples of locally profinite groups are discrete groups and p-adic Lie group. Non-examples are real Lie groups which have no small subgroup property.

In a locally profinite group, a closed subgroup is locally profinite, and every compact subgroup is contained in an open compact subgroup.