Isomorphism Preserves Groups/Proof 2

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Theorem

Let $\left({S, \circ}\right)$ and $\left({T, *}\right)$ be algebraic structures.

Let $\phi: \left({S, \circ}\right) \to \left({T, *}\right)$ be an isomorphism.


If $\left({S, \circ}\right)$ is a group, then so is $\left({T, *}\right)$.


Proof

An isomorphism is an epimorphism.

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

$\blacksquare$