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The term pro-p-group for a prime number pis 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.

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
profinite group
pronilpotent group