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Math Help - homomorphism

  1. #1
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    homomorphism

    G = Z_4 x Z_4

    prove that the map theta: Z_4 x Z_4 --> Z_4 defined by theta(([a],[b])) = [b] is a homomorphism ONTO Z_4.

    what is the kernel of theta? Show that the quotient group G/<([1],[0])> is isomorphic to Z_4
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by tas10 View Post
    G = Z_4 x Z_4

    prove that the map theta: Z_4 x Z_4 --> Z_4 defined by theta(([a],[b])) = [b] is a homomorphism ONTO Z_4.

    what is the kernel of theta? Show that the quotient group G/<([1],[0])> is isomorphic to Z_4
    Where's the work? It's just as easy to prove in general the projection g,h)\mapsto g" alt="\pi:G\times H\to Gg,h)\mapsto g" /> is an epimorphism.
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