Inverse 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]
This article is about a general term. A list of important particular cases (instances) is available at Category: Subgroup properties satisfying inverse image condition
Definition
Symbol-free definition
A subgroup property is said to satisfy the inverse image condition if, for any homomorphism of groups, the inverse image of a subgroup satisfying the property in the group on the right, satisfies the property in the group on the left.
Definition with symbols
Let be a subgroup property. We say that
satisfies the inverse image condition if for any homomorphism
, the following holds: whenever
is a subgroup satisfying
in
,
satisfies
in
.