Trivial homomorphism of groups

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

Let $G$, $H$ be groups and $e_{H}$ be the identity of $H$. Then the map $\varphi :G\to H$ sending every $g\in G$ to $e_{H}$ is a homomorphism of groups, called the trivial homomorphism.