Isomorphism Preserves Groups/Proof 2
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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.
$\blacksquare$