# orbit

Let $G$ be a group, $X$ a set, and $\cdot :G\times X\u27f6X$ a group action^{}. For any $x\in X$, the orbit of $x$ under the group action is the set

$$\{g\cdot x\mid g\in G\}\subset X.$$ |

Title | orbit |
---|---|

Canonical name | Orbit |

Date of creation | 2013-03-22 12:12:20 |

Last modified on | 2013-03-22 12:12:20 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 6 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 20M30 |