 Locally profinite group

A locally profinite group is a Hausdorff, locally compact, totally disconnected topological group. It has a neighbourhood basis at the identity consisting of compact-open subgroups. In smooth representation theory this is also called an $\ell$-group; that terminology is unrelated to a lattice-ordered group.

A **locally profinite group** is a type of group that is constructed from profinite groups, which are groups that are isomorphic to an inverse limit of finite groups. Formally, a locally profinite group can be defined as a group \( G \) that has a neighborhood basis at the identity consisting of open subgroups that are profinite.