Regular group action

Definition
A regular group action of a group on a nonempty set is a group action that satisfies the following euqivalent conditions:


 * 1) It is both transitive and semiregular.
 * 2) For any two (possibly equal) elements of the set, there is a unique group element taking the first to the second.
 * 3) It is equivalent to the left-regular group action: the action of a group on itself by left multiplication.

Weaker properties

 * Stronger than::Transitive group action
 * Stronger than::Faithful group action
 * Stronger than::Semiregular group action

Related properties

 * 2-regular group action