Free, open-source online mathematics for students, teachers and workers

Two groups $G$ and $G'$ are isomorphic if there is a bijection $\varphi$ from $G$ to $G'$ which satisfies $\varphi(x)=\varphi(y)$ for all $x$, $y\in G$. The function $\varphi$ is called an isomorphism between $G$ and $G'$