Groups. Monomorphism equivalents.

$\text{monomorphism}⟺\text{kernel}=\{e\}⟺\text{set-injective}$

Let $G$ and $H$ be groups, and $\phi :G\to H$ be a group homomorphism.

The following are equivalent:

1. $\phi$ is a monomorphism.
2. $\ker \phi =\{e_G\}$.
3. $\phi$ is injective as a set-function.