# Isomorphism

## Formal Definition

**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]}

## See also

## References

- ↑ Pinter, Charles C. A Book of Abstract Algebra. Dover ed. Mineola, N.Y: Dover Publications, 2010.