# Burnside $p$-$q$ theorem

Any group whose order is divisible by only two distinct primes is solvable. (These two distinct primes are the $p$ and $q$ of the title.)

It follows that if $G$ is a non-abelian finite simple group, then $|G|$ must have at least three distinct prime divisors^{}.

Title | Burnside $p$-$q$ theorem |
---|---|

Canonical name | BurnsidePqTheorem |

Date of creation | 2013-03-22 13:15:58 |

Last modified on | 2013-03-22 13:15:58 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 8 |

Author | yark (2760) |

Entry type | Theorem |

Classification | msc 20D05 |