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Math Help - Homomorphic images of Z15.

  1. #1
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    Homomorphic images of Z15.

    What are all the homomorphic images of Z15 (up to isomorphism)?
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  2. #2
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    Quote Originally Posted by o&apartyrock View Post

    What are all the homomorphic images of Z15 (up to isomorphism)?
    a homomorphic image of a group G is a group in the form G/K, where K is a normal subgroup of G. in your case G=\mathbb{Z}/15 \mathbb{Z} is abelian. so K is any subgroup of G. find the subgroups of G and then

    see what G/K are! the final answer is:

    Spoiler:

    (0), \ G, \ \mathbb{Z}/3 \mathbb{Z}, \ \mathbb{Z}/5 \mathbb{Z}.
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