# Homomorphism

## Formal Definition

**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]}

## See also

## References

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