Groupprops, The Group Properties Wiki (pre-alpha)
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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

Contents 1 Definition 1.1 Symbol-free definition 1.2 Definition with symbols

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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 p is said to satisfy the image condition if whenever is a surjective homomorphism and satisfies property p in G, then φ(H) satisfies property p in K.