Definition:Isomorphism (Abstract Algebra)

Definition
An isomorphism is a homomorphism which is a bijection.

That is, it is a mapping which is both a monomorphism and an epimorphism.

An algebraic structure $\struct {S, \circ}$ is isomorphic to another algebraic structure $\struct {T, *}$ there exists an isomorphism from $\struct {S, \circ}$ to $\struct {T, *}$, and we can write $S \cong T$ (although notation may vary).

Also see

 * Definition:Automorphism (Abstract Algebra)