Characteristic 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
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VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions


Symbol-free definition

A subgroup property is said to be characteristic core-closed if whenever a subgroup has the proeprty in the whole group, so does its characteristic core (viz the largest characteristic subgroup contained inside it).

Definition with symbols

A subgroup property p is said to be characteristic core-closed if whenever H satisfies property p in G, and K is the characteristic core of H, K satisfies property p in G.

Relation with other metaproperties

Stronger metaproperties

Related metaproperties