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Math Help - Basic Isomorphic Systems

  1. #1
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    Basic Isomorphic Systems

    I had some trouble with this problem:

    Is <J_{4}, +_{4}> isomorphic to <{ 1,-1,i,-i} , *>?

    I made product tables but I'm having a hard time identifying the isomorphic relationship. Is there one?
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  2. #2
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    Quote Originally Posted by jameselmore91 View Post
    I had some trouble with this problem:

    Is <J_{4}, +_{4}> isomorphic to <{ 1,-1,i,-i} , *>?

    I made product tables but I'm having a hard time identifying the isomorphic relationship. Is there one?

    If I understand correctly your symbols, we have two cyclic groups of order 4, one written additively (addition modulo 4) and the other one written multiplicatively (complex multiplication). Identify a generator in each and define a map between these two generators, mapping powers of one to powers (or multiples) of the other...

    Tonio
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