Definition:Group Epimorphism

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Let $\struct {G, \circ}$ and $\struct {H, *}$ be groups.

Let $\phi: G \to H$ be a (group) homomorphism.

Then $\phi$ is a group epimorphism if and only if $\phi$ is a surjection.

Also see

Linguistic Note

The word epimorphism comes from the Greek morphe (μορφή) meaning form or structure, with the prefix epi- meaning onto.

Thus epimorphism means onto (similar) structure.