Definition:Isomorphism (Abstract Algebra)/Group Isomorphism

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

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

Then $\phi$ is a group isomorphism $\phi$ is a bijection.

That is, $\phi$ is a group isomorphism $\phi$ is both a monomorphism and an epimorphism.

If $G$ is isomorphic to $H$, then the notation $G \cong H$ can be used (although notation varies).

Also known as
Isomorphism as defined here is known by some authors as simple isomorphism.

Also see

 * Definition:Isomorphism (Abstract Algebra)