# Join-closure operator

From Groupprops

This article defines a subgroup property modifier (a unary subgroup property operator) -- viz an operator that takes as input a subgroup property and outputs a subgroup propertyView a complete list of subgroup property modifiers OR View a list of all subgroup property operators (possibly with multiple inputs)

## Definition

The **join-closure operator** takes a subgroup property and outputs the property of being a subgroup that can be expressed as a join of (possibly infinitely many) subgroups, each having property in the whole group.