# Algebraically closed group

From Groupprops

## Definition

A group is termed **algebraically closed** if every finite set of equations and inequations in the group that is consistent (i.e., the system has a solution in some bigger group containing the group) has a solution in the group itself.

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

## Relation with other properties

### Weaker properties

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

simple group | algebraically closed implies simple | simple not implies algebraically closed | |FULL LIST, MORE INFO |