regular group action

Let G be a group actionMathworldPlanetmath on a set X. The action is called if for any pair α,βX there exists exactly one gG such that gα=β. (For a right group action it is defined correspondingly.)

A key example of a regularPlanetmathPlanetmath action is the regular representationPlanetmathPlanetmath of a group, with action given by group multiplicationPlanetmathPlanetmath.

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