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Proving f inverse is homomorphic

  1. Sep 15, 2010 #1
    I'm trying to show:

    If f: S -> S' is an isomorphism of <S, *> with <S', *'>, then f^(-1) is homomorphic.

    My take:

    So I have to show that f^(-1)(x' *' y') = f^(-1)(x') * f^(-1)(y').

    Since f is bijective (onto, more precisely) I know that f^(-1)(x') = x and f^(-1)(y') = y. So f^(-1)(x') * f^(-1)(y') = xy.

    How can I simplify f^(-1)(x' *' y') though?

    Thanks.
     
  2. jcsd
  3. Sep 15, 2010 #2
    EDIT: Nevermind, that's not right.

    Sorry about not using latex, by the way. I was writing from a mobile device.
     
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