# example of divisible group

Let $G$ denote the group of rational numbers^{} taking the operation^{} to be addition^{}. Then for any $\frac{p}{q}\in G$ and $n\in {\mathbb{Z}}^{+}$, we have $\frac{p}{nq}\in G$ satisfying $n\frac{p}{nq}=\frac{p}{q}$, so the group is divisible.

Title | example of divisible group |
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Canonical name | ExampleOfDivisibleGroup |

Date of creation | 2013-03-22 13:47:20 |

Last modified on | 2013-03-22 13:47:20 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 4 |

Author | mathcam (2727) |

Entry type | Example |

Classification | msc 20K99 |