Hello everybody!(adsbygoogle = window.adsbygoogle || []).push({});

I've just started with studying group homorphisms and tensor products, so i am still not very sure if i undertstand the subject correct. I am stuck with a question and i would ask you for some help or hints how to proceed...

What i have to do is to describe ##Hom(\mathbb{Q}/\mathbb{Z},\mathbb{Q})## and ##Hom(\mathbb{Q},\mathbb{Q}/\mathbb{Z})##. I know that both ##\mathbb{Q}/\mathbb{Z}## and ##\mathbb{Q}## are abelian groups, ##\mathbb{Q}/\mathbb{Z}## as a ##\mathbb{Z}##-module is finitely generated, but ##\mathbb{Q}## as a ##\mathbb{Z}##-module is not finitely generated.

Can anybody help me with this problem? How is it meant "to describe the groups of homomorphisms"?

Thank you in advance!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Groups of homomorphisms of abelian groups

Tags:

Loading...

Similar Threads - Groups homomorphisms abelian | Date |
---|---|

Is this homomorphism, actually isomorphism of groups? | Dec 6, 2013 |

Homomorphisms of Cyclic Groups | Dec 12, 2012 |

Group Homomorphism Question. | Nov 12, 2012 |

Group homomorphism | Aug 16, 2011 |

Homomorphism on modulo groups | Nov 7, 2010 |

**Physics Forums - The Fusion of Science and Community**