Right-realized 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

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: Right-realized subgroup properties


Symbol-free definition

A subgroup property is said to be right-realized if every group has a subgroup that satisfies the property in it.

Definition with symbols

A subgroup property p is said to be right-realized if for any group G, there is a subgroup H of G such that H satisfies p in G.

In terms of the right realization operator

A subgroup property is right realized if the group property obtained by applying the right realization operator to it is the tautology, viz the property of being any group.

Relation with other metaproperties

Stronger metaproperties


Related metaproperties