Group metaproperty

Definition
A group metaproperty is a map from the collection of all group properties (viz., the group property space) to the two-element set (true, false). Those group properties which get mapped to true are said to have or possess the group metaproperty; those which get mapped to false are said to not have or not possess the group metaproperty.

Examples
An example of a group metaproperty is being quotient-closed. A group property is termed quotient-closed or Q-closed if whenever a group satisfies the properties, so does every quotient of the group. Note that for any group property it either is Q-closed or is not Q-closed.