Proof of a theorem regarding group homomorphisms and kernels I am looking for a proof of the following theorem:
"Let $H<G$ then $H\unlhd G$ $\iff$ there exists a group $K$ and a group homomorphism: $\phi : G \rightarrow K$ such that $ker(\phi) = H$
There is one on a french wikipedia page but I find it incomprehensible.
Edit I unfortunately don't know how to suppress questions from this site, I've found the answer I nee**
If anyone is interested, here's the link: https://proofwiki.org/wiki/Kernel_is_Normal_Subgroup_of_Domain

The forward direction will be done by considering $K=G/H$ and for the converse part, kernel of a group homomorphism is always a normal subgroup.
