# Normal subgroups, quotient groups

## Homework Statement

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

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

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