Algebraically closed group
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
|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|