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Non-Abelian group of Order 12

  1. Dec 19, 2008 #1
    Thank you for your time!

    1. The problem statement, all variables and given/known data
    Prove that Z/3 X|[tex]\alpha[/tex] Z/4 is a non-abelian group of order 12 which it is not isomorphic to A4 or to D6

    X|][tex]\alpha[/tex] is supposed to be the sign for semi direct product.

    2. Relevant equations

    Z/3 X|[tex]\alpha[/tex] Z/4=<a,b / a4=b3=1, aba=a>
    A4=<a,b / a3=b2=1, aba=ba-1b>
    D6=<a,b / a2=b2=1, bab-1=a-1>

    3. The attempt at a solution

    I am just having issues wrapping my head around Z/3 X|[tex]\alpha[/tex] Z/4, I read somewhere that Z/3 X|[tex]\alpha[/tex] Z/4 = {x,y / x[tex]\in[/tex]Z/3 and y[tex]\in[/tex]Z/4} with the operation (x1,y1)(x2,y2)=....and thats where I am stuck.
  2. jcsd
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