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Homework Help: Normal subgroups, quotient groups

  1. Apr 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Let G be the group {[tex]
    \begin{bmatrix}{a}&{b}\\{0}&{c}\end{bmatrix}
    [/tex] | a, b, c are in [tex]Z_p[/tex] with p a prime}
    Then let K = {[tex]
    \begin{bmatrix}{1}&{b}\\{0}&{1}\end{bmatrix}
    [/tex] | b in [tex]Z_p[/tex]}

    The map P: G --> Z*p x Z*p is defined by
    P( [tex]
    \begin{bmatrix}{a}&{b}\\{0}&{c}\end{bmatrix}
    [/tex] ) = (a, c)

    prove P is a group homomorphism.


    I thought it would suffice to show that P(G1)P(G2)=P(G1G2) for some G1 G2 in G, and that this is true since (a1,c1)(a2,c2)=(a1a2,c1c2) -- Is this correct

    Thank you so much for any help!
     
    Last edited: Apr 13, 2010
  2. jcsd
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