Group homomorphism factors through group

This article is about a basic definition in group theory. The article text may, however, contain advanced material.
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Definition

Suppose $G$, $H$, $K$ are groups and $\theta :G\to H$ is a group homomorphism. We say $\theta$ factors through $K$ if there exist group homomorphisms $\alpha :G\to K$ and $\beta :K\to H$ such that $\theta =\beta \circ \alpha$.