Normal core-closed subgroup property

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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

Definition

Symbol-free definition

A subgroup property is said to be normal core-closed if whenever a subgroup has the property in the whole group, its normal core also has the property.

Definition with symbols

A subgroup property p is said to be normal core-closed if whenever H satisfies property p in G, the normal core H_G also satisfies p in G.

Relation with other metaproperties

Stronger metaproperties

Related metaproperties