# Right-realized subgroup property

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]

## 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.