Definition:Group Epimorphism

Definition

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

• Definition:Epimorphism (Abstract Algebra)

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.

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 7.1$. Homomorphisms
• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Quotient Groups
• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Group Homomorphism and Isomorphism: $\S 67$
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 47.5 \ \text{(b)}$ Homomorphisms and their elementary properties