Definition:Group Homomorphism/Also defined as

Group Homomorphism: Also defined as

In their definition of a group homomorphism, some sources demand further that $\map \phi {e_G} = e_H$, where $e_G$ and $e_H$ are the identity elements of $G$ and $H$, respectively.

However, this condition is superfluous, as shown on Group Homomorphism Preserves Identity.

Sources

• 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): $\S 3.2$: Groups; the axioms