Suppose $F : G \rightarrow K $ is a group epimorphism with $G$ finitely generated and $K$ finitely presented. Then, show that $H := \ker F$ is the normal closure of a finite subset in $H$.
My attempt
Since $F$ is surjective, so $G/H \cong K$, say $\varphi : G/H \rightarrow K $.
So, I think since $K$ has a finite relation set $R_K$, $R_k$ is the key point..
However, I don't have any idea. How to solve this problem?
Thanks.