# Isomorphism

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Definition. Let $G_1$ and $G_2$ be groups. A bijective function $f : G_1 \to G_2$ with the property that for any two elements $a$ and $b$ in $G_1$, $$f(ab) = f(a) \cdot f(b)$$ is called an isomorphism from $G_1$ to $G_2$. If this isomorphism exists, we say that $G_1$ is isomorphic to $G_2$, written $G_1 \cong G_2$.[1]