# conjugacy class

Let $G$ a group, and consider its operation^{} (action) on itself give by conjugation^{}, that is, the mapping

$$(g,x)\mapsto gx{g}^{-1}$$ |

Since conjugation is an equivalence relation^{}, we obtain a partition^{} of $G$ into equivalence classes^{}, called *conjugacy classes ^{}*. So, the conjugacy class of $X$ (represented ${C}_{x}$ or $C(x)$ is given by

$${C}_{x}=\{y\in X:y=gx{g}^{-1}\text{for some}g\in G\}$$ |

Title | conjugacy class |
---|---|

Canonical name | ConjugacyClass1 |

Date of creation | 2013-03-22 14:01:39 |

Last modified on | 2013-03-22 14:01:39 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 5 |

Author | drini (3) |

Entry type | Definition |

Classification | msc 20E45 |