- #1

polarbears

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## Homework Statement

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]

## Homework Equations

## 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?