regular group action

Let $G$ be a group action on a set $X$. The action is called if for any pair $\alpha ,\beta \in X$ there exists exactly one $g\in G$ such that $g\cdot \alpha =\beta$. (For a right group action it is defined correspondingly.)

A key example of a regular action is the regular representation of a group, with action given by group multiplication.

Title	regular group action
Canonical name	RegularGroupAction
Date of creation	2013-03-22 13:21:35
Last modified on	2013-03-22 13:21:35
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	7
Author	mathcam (2727)
Entry type	Definition
Classification	msc 20A05
Related topic	GroupAction