Isomorphism Preserves Groups/Proof 2

Theorem

Let $\struct {S, \circ}$ and $\struct {T, *}$ be algebraic structures.

Let $\phi: \struct {S, \circ} \to \struct {T, *}$ be an isomorphism.

If $\struct {S, \circ}$ is a group, then so is $\struct {T, *}$.

Proof

An isomorphism is an epimorphism.

The result follows as a direct corollary of Epimorphism Preserves Groups.

$\blacksquare$