>[!success] Theorem >If $\phi : G \rightarrow G'$ is a [[Group|group]] [[Maps and Induced Structures - Functions, Pushforwards and Pullbacks|homomorphism]], then the [[Quotient Group|quotient group]] of $G$ with the kernel of $\phi$ is [[Mappings between Groups|isomorphic]] to $G'$ $G/ker(\phi)\cong\phi(G).$