Right-realized subgroup property

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
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This article is about a general term. A list of important particular cases (instances) is available at Category: Right-realized subgroup properties

Definition

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

• Trivially true subgroup property
• Identity-true subgroup property
• Trim subgroup property
• t.i. subgroup property

Opposites

• Right-unrealized subgroup property is a subgroup property that is not right-realized

Related metaproperties

• Left-realized subgroup property