Definition:Isomorphism (Abstract Algebra)

An isomorphism is a homomorphism which is a bijection.

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