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Math Help - homomorphism

  1. #1
    Member vernal's Avatar
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    homomorphism

    if has monomorphism , and N is abelian
    then is homomorphism??
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  2. #2
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    Re: homomorphism

    f^{-1} only makes sense on f(N), since there's no unique way to define f^{-1}(g) for g \in G\setminus f(N).

    but if we are restricting our attention to f(N), then f^{-1} is more than just a homomorphism, it's an isomorphism (because if f:N \to G is a monomorphism, f:N \to f(N) is an isomorphism).
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