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Math Help - Homomorphism

  1. #1
    Junior Member mathemanyak's Avatar
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    Homomorphism

    find all homomorphism form Z6 to Z4?
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  2. #2
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    Quote Originally Posted by mathemanyak View Post
    find all homomorphism form Z6 to Z4?
    Hint: Any homomorphism is completely determined on [1]_6 because \left< [1]_6\right> = \mathbb{Z}_6.

    Now there are four possbilites:
    [1]_6\mapsto [0]_4
    [1]_6\mapsto [1]_4
    [1]_6\mapsto [2]_4
    [1]_6\mapsto [3]_4

    Now check which ones are isomorphisms.
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  3. #3
    Junior Member mathemanyak's Avatar
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    help!

    How can we show that?Please help!
    How can I Understand which one is isomorp?
    Last edited by mathemanyak; July 30th 2008 at 05:00 AM.
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