# Permuting upper join-closed subgroup property

From Groupprops

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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 metapropertyVIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

## Definition

A subgroup property is termed a **permuting upper join-closed subgroup property** if for any subgroup of a group and two intermediate subgroups and satisfying:

- satisfies in both and , and
- , i.e., they are permuting subgroups,

we must have that satisfies in the join of subgroups which in this case is also the product of subgroups .