# Conjugate-join-closed subgroup property

From Groupprops

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 metapropertyVIEW 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 termed **conjugate-join-closed** if the join of a nonempty collection of conjugate subgroups satisfying , also satisfies . Note that any two subgroups in the collection must be conjugate; however, the collection need not include all members of that conjugacy class of subgroups.