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Math Help - Another integers mod 4 question

  1. #1
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    Another integers mod 4 question

    Use the first isomorphism theorem to show the following:

    Z/(4Z) is isomorphic to Z4.

    There are other ones to solve I'm just using this as an example so I can figure out the thinking behind it. I can prove it with multiplication tables, but in reference to the F.I.T. I'm not sure how to start.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by DanielThrice View Post
    Use the first isomorphism theorem to show the following:

    Z/(4Z) is isomorphic to Z4.

    There are other ones to solve I'm just using this as an example so I can figure out the thinking behind it. I can prove it with multiplication tables, but in reference to the F.I.T. I'm not sure how to start.
    Possibly because \theta:\mathbb{Z}\to\mathbb{Z}_4:x\mapsto \left(x\text{ mod }4\right) a surjective homomorphism. What's \ker\theta?
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