The intersect-all operator is an operator that takes as input a subgroup property and outputs the subgroup-defining function that sends a group to the intersection of all subgroups of it that satisfy the property.
Definition with symbols
Let be a subgroup property. The intersect-all operator applied to outputs the following subgroup-defining function :
where varies over all subgroups of satisfying property in .
Important instances of application of the intersect-all operator: