Commutator-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 p is termed commutator-closed if the commutator of any two subgroups, each of which has property p in the whole group, also has property p in the whole group.

Definition with symbols

A subgroup property p is termed commutator-closed if, given any group G and subgroups H,K \le G such that H and K both satisfy property p in G, the commutator [H,K] also satisfies property p in G.

Relation with other metaproperties

Stronger metaproperties

Related metaproperties