# stabilizer

Let $G$ be a group, $X$ a set, and $\cdot :G\times X\u27f6X$ a group action^{}. For any subset $S$ of $X$, the stabilizer^{} of $S$, denoted $\mathrm{Stab}(S)$, is the subgroup^{}

$$\mathrm{Stab}(S):=\{g\in G\mid g\cdot s\in S\text{for all}s\in S\}.$$ |

The stabilizer of a single point $x$ in $X$ is often denoted ${G}_{x}$.

Title | stabilizer |
---|---|

Canonical name | Stabilizer |

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

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

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 7 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 20M30 |

Classification | msc 16W22 |

Synonym | isotropy subgroup |