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Math Help - isomorphism

  1. #1
    Super Member
    Joined
    Aug 2009
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    isomorphism

    may i know what does it mean by a group is isomorphic to itself by the identity function?

    thanks
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  2. #2
    Senior Member
    Joined
    Nov 2008
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    Paris
    Posts
    354
    Hi

    It just means that if you consider the identity function id_G, where (G,.) is your group, then:

    id_G\ :\ G\rightarrow G\ :\ x\mapsto x is a morphism, that is id_G(a.b)=id_G(a).id_G(b) for all a,b\in G.

    This assertion is quite trivial, since the equality above means a.b=a.b, which is obviously true.
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