# Pro-p-group

From Groupprops

## Definition

The term **pro--group** for a prime number 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 , each equipped with the discrete topology.

Note that the term p-group used in isolation could refer to a finite or infinite -group, but pro--groups are typically defined to only allow finite -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 |