p-adic Lie group

Summary

A $p$-adic Lie group is a topological group that is also an analytic manifold over the field $\Q_p$ of p-adic numbers, with analytic group operations. It is the $p$-adic analogue of a real Lie group. Such groups are totally disconnected, so their structure is studied through compact open subgroups, which are pro-p groups up to finite index. They appear as Galois groups in number theory and as the groups $G(\Q_p)$ of points of algebraic groups.