Algebraically closed group

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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

Facts