homomorphism

Definition

Suppose groups $G$ and $G'$, then a homomorphism is a map $\varphi: G \to G'$ such that for all $a,b \in G$,

Notes

• not to be confused with homeomorphism
• see isomorphism, which includes an additional requirement of bijection

References

1. M. Artin, Algebra, 2. ed. Boston, Mass. Munich: Pearson Education, Prentice Hall, 2011, pp. 47-48.