Quotient group and epimorphism

Question

I wonder if the statement below is right: "If there is an epimorphism from $G$ to $H$, we can say that $H$ is a quotient group of $G$."

Answer 1

Yes! this is the first isomorphism Theorem.

Theorem: Let $H,K$ be two groups and $\varphi:H\rightarrow K$ be a homomorphism. Then, $$H/\ker\varphi \cong Im\varphi$$

In particular when $\varphi$ is onto you have that $K$ is (isomorphic to) a quotient.