Join-closure operator

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 property

View 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 $p$ and outputs the property of being a subgroup that can be expressed as a join of (possibly infinitely many) subgroups, each having property $p$ in the whole group.