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Non-Abelian group of Order 12

  • Thread starter nobody56
  • Start date
11
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Thank you for your time!

1. Homework Statement
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. Homework 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.
 

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