# Homomorphism

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Definition. If $F$ and $G$ are groups, a homomorphism from $G$ to $H$ is a function $f : G \to H$ such that for any two elements $a$ and $b$ in $G$, $$f(ab) = f(a) \cdot f(b)$$ If there exists a homomorphism from $G$ onto $H$, we say that $H$ is a homomorphic image of $G$.[1]