# 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 |