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Homework Help: Find an isomorphism between U_7 and Z_7

  1. Jan 28, 2009 #1
    1. The problem statement, all variables and given/known data

    There is an isomorphism of [tex]U_{7}[/tex] with [tex]Z_{7}[/tex] in which [tex]\zeta[/tex]=[tex]e^{(i2\pi}/7[/tex][tex]\leftrightarrow[/tex]4. Find the element in [tex]Z_{7}[/tex] to which [tex]\zeta^{m}[/tex] must correspond for m=0,2,3,4,5, and 6.

    2. Relevant equations



    3. The attempt at a solution
    [tex]\zeta^{0}[/tex]=0
    [tex]\zeta^{2}[/tex]=4+[tex]_{7}[/tex]4=1
    [tex]\zeta^{3}[/tex]=[tex]\zeta^{2}[/tex][tex]\zeta^{1}[/tex]=4+[tex]_{7}[/tex]1=-2

    I don't know if I'm doing this right?
     
  2. jcsd
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