Algebraically closed group
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 properties
VIEW 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 |