This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
A subgroup property is said to satisfy the image condition if, under any surjective homomorphism, the image of a subgroup satisfying the property in the source group, again satisfies the property in the target group.
Definition with symbols
A subgroup property is said to satisfy the image condition if whenever is a surjective homomorphism and satisfies property in , then satisfies property in .