homomorphism from decomposition group to Galois group

Question

Let K be a number field that is Galois over $\Bbb Q$ with group $G = Gal(K/\Bbb Q)$. Fix a prime $\mathfrak p ⊂ \mathcal O_K$ lying over $p ∈ \Bbb Z$.Let $D_{\mathfrak p}$ be its decomposition group.

Studying Stein's Algebraic Number Theory book, I came across this sentence:

I don't see why it is the case, any reference or insights about this homomorphism?

Thank you for any help.