# Homework Help: Notation. galois theory problem

1. Mar 10, 2010

### cap.r

1. The problem statement, all variables and given/known data
let $$K$$ be a field and $$K(t)$$ the rational functions in $$t$$.
Show that $$\ G=Aut_K K(t)$$ $$\cong$$ $$\ GL(2,K)$$

2. Relevant equations

I have the fundamental Galois theorem to work with and normal subgroups. but we haven't done splitting fields.

3. The attempt at a solution
I am really just unsure of how to proceed here. I am guessing $$GL(2,K)$$ is just the 2x2 matrices with nonzero determinants and elements in $$K$$. and if that's true I don't really know what to do.

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