Profinite group

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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