Inverse image condition
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
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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
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 .