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Homework Help: Determine if morphism, find kernel and image

  1. Nov 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Determine if the following is a group morphism. Find the kernel and the image if so.
    [tex]f:C_{2} \times C_{3} \rightarrow S_{3}[/tex] where [tex]f(h^{r},k^{s})=(1,2)^{r} \circ (123)^{s}[/tex]

    2. Relevant equations

    3. The attempt at a solution
    I'm stuck on the morphism part. So I know I need to show that [tex] f(h^{r+x},k^{s+y})=(1,2)^{r+x} \circ (123)^{s+y} = (12)^{r} \circ (123)^{s} \circ (12)^{x} \circ (123)^{y}[/tex]
    but I'm not sure how to do that.
    Also could someone check my set up?
  2. jcsd
  3. Feb 15, 2010 #2
    Been awhile and no response
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