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 RegularGroupAction 2013-03-22 13:21:35 2013-03-22 13:21:35 mathcam (2727) mathcam (2727) 7 mathcam (2727) Definition msc 20A05 GroupAction