Pro-p-group

Definition
The term pro-$$p$$-group for a prime number $$p$$is typically used to refer to a topological group that can be described as the inverse limit of an inverse system of finite p-groups for that prime $$p$$, each equipped with the discrete topology.

Note that the term p-group used in isolation could refer to a finite or infinite $$p$$-group, but pro-$$p$$-groups are typically defined to only allow finite $$p$$-group in the inverse system whose limit is being taken.