Profinite group
Definition
As an abstract group
A profinite group is a group that arises as the inverse limit of an inverse system of finite groups.
As a topological group
A profinite group is a group that arises as the inverse limit of an inverse system of finite groups, viewed as topological groups with the discrete topology.
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
This is a variation of finite group|Find other variations of finite group |
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| Finite group | finite implies profinite | profinite not implies finite | |FULL LIST, MORE INFO |