# Regular group action

From Groupprops

This article defines a group action property or a property of group actions: a property that can be evaluated for a group acting on a set.

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## Definition

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

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