## A Group Homomorphism is Injective if and only if Monic

## Problem 243

Let $f:G\to G’$ be a group homomorphism. We say that $f$ is **monic** whenever we have $fg_1=fg_2$, where $g_1:K\to G$ and $g_2:K \to G$ are group homomorphisms for some group $K$, we have $g_1=g_2$.

Then prove that a group homomorphism $f: G \to G’$ is injective if and only if it is monic.

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