# Restricted direct product of finite groups

From Groupprops

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 propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

A group is termed a **restricted direct product of finite groups** if it is isomorphic to the restricted external direct product of a bunch of finite groups.

## Relation with other properties

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Residually finite group | every non-identity element is outside some normal subgroup of finite index | |||

Locally finite group | every finitely generated subgroup is finite |