Group action property

Symbol-free definition
A group action property is a map from the collection of all group actions to the two-element set (true, false) with the property that if one group acts similarly on a set to another group on another set, then they get mapped to the same thing.

Important examples of group properties
Being transitive is a group action property: a group action is transitive if, for any two elements of the set being acted on, there is an element of the group taking one element to the other.