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Math Help - normal subgroup, homomorphism

  1. #1
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    normal subgroup, homomorphism

    Suppose f: G \rightarrow H is a group homomorphism, N \triangleleft G, and \text{ker}(f)  \leq N.

    Prove that
    G/N \cong f(G)/f(N).

    I don't see how to do this. Any hints would be nice. Thank you.
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  2. #2
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    Quote Originally Posted by maya8913 View Post
    Suppose f: G \rightarrow H is a group homomorphism, N \triangleleft G, and \text{ker}(f)  \leq N.

    Prove that
    G/N \cong f(G)/f(N).

    I don't see how to do this. Any hints would be nice. Thank you.
    use the fact that f(G)/f(N)=(G/\ker f)/(N/\ker f)=G/N
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