# multiply transitive

Let $G$ be a group, $X$ a set on which it acts. Let ${X}^{(n)}$ be the set of order $n$-tuples of distinct elements of $X$. This is a $G$-set by the diagonal action:

$$g\cdot ({x}_{1},\mathrm{\dots},{x}_{n})=(g\cdot {x}_{1},\mathrm{\dots},g\cdot {x}_{n})$$ |

The action of $G$ on $X$ is said to be $n$-transitive^{} if it acts transitively on ${X}^{(n)}$.

For example, the standard action of ${S}^{n}$, the symmetric group^{}, is $n$-transitive, and the
standard action of ${A}_{n}$, the alternating group^{}, is $(n-2)$-transitive.

Title | multiply transitive |
---|---|

Canonical name | MultiplyTransitive |

Date of creation | 2013-03-22 13:16:37 |

Last modified on | 2013-03-22 13:16:37 |

Owner | bwebste (988) |

Last modified by | bwebste (988) |

Numerical id | 5 |

Author | bwebste (988) |

Entry type | Definition |

Classification | msc 20B20 |

Synonym | $n$-transitive |