1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

  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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook