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Math Help - isomorphisms..direct product?

  1. #1
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    Exclamation isomorphisms..direct product?

    Say that [+] = external direct product of groups.
    Given that,

    Suppose that G is isomorphic to K and H is isomorphic to J. Prove that G[+]H is isomorphic to K[+]J
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    Super Member Rebesques's Avatar
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    If \phi:G\rightarrow K, \ \psi:H\rightarrow J are the isomorphisms, consider the map \omega:G\oplus H\rightarrow K\oplus J defined by \omega(g\oplus h)=\phi(g)\oplus\psi(h). Show this is an isomorphism.
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  3. #3
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    Quote Originally Posted by cowgirl123 View Post
    Say that [+] = external direct product of groups.
    Given that,

    Suppose that G is isomorphic to K and H is isomorphic to J. Prove that G[+]H is isomorphic to K[+]J
    See here
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