Image condition
From Groupprops
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]
Definition
Symbol-free definition
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
.