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Math Help - Question on group mapping

  1. #1
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    Question on group mapping

    I working on a problem I can do since I have done many of this forum. However, I don't understand the group mapping:

    G is a group and we are mapping G to G by g\to g^{-1}.

    How does this mapping work?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Question on group mapping

    Quote Originally Posted by dwsmith View Post
    How does this mapping work?
    I don't understand the exact meaning of your question. The mapping \psi:G\to G , \psi(g)=g^{-1} is well defined (for every g\in G there exists its inverse g^{-1} and it is unique). Besides, \psi(ab)=(ab)^{-1}=b^{-1}a^{-1}=\psi(b)\psi(a) for all a,b\in G .
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    Re: Question on group mapping

    Quote Originally Posted by FernandoRevilla View Post
    The mapping \psi:G\to G , \psi(g)=g^{-1}
    Your reply helped. This is what I needed to see.
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