That's algebra!

Therefore is a normal subgroup of .

is surjective by definition of , a group homomorphism because and injective because .

We have found an isomorphism between and .

Consider a,b)\mapsto b" alt="\phi: G\rightarrow G_2a,b)\mapsto b" /> .

, so is an homomorphism, which is surjective by definition of .

Moreover, .

Hence , and we can conclude .