> [!NOTE] **Definition** (Group Isomorphism) > > Let $(G, \diamond)$ and $(H, *)$ be [[Group|groups]]. Let $\phi:G\to H$ be a [[Homomorphism|homomorphism]]. Then $\phi$ is an isomorphism iff it is [[Bijection|bijective]]. > > **Notation**: In this case we say that $G$ and $H$ are isomorphic, denoted $G \cong H.$ # Properties Isomorphism is an equivalence relation.