Let $G := ($$\mathbb{Z}_4$$, +)$ and $N := ($$\mathbb{Z}_2$$, +)$.
If $N$ is a normal subgroup of $G$, is $G \to G /N$ an epic morphism?
If yes, how can you prove this?
My attempt:
$G/N:=\{gN : g \in G\}$
Shouldn't this be:
$$\mathbb{Z}_2 + 0 = \{0, 1\} \\ \mathbb{Z}_2 + 1 = \{1, 2\} \\ \mathbb{Z}_2 + 2 = \{2, 3\} \\ \mathbb{Z}_2 + 3 = \{3, 0\} \\$$ ?