Group Isomorphism

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Definition (Group Isomorphism)

Let $(G,\cdot)$ and $(H,\times)$ be groups. We say that the function $f:G\to H$ is a group $\textdef{isomorphism}$ if $f$ is a bijection and $f$ preserves the group structures, which means $f(a\cdot b)=f(a)\times f(b)$ for every $a,b\in G$. We say that $G$ and $H$ are isomorphic groups, and write $G\approx H$ if there exists an isomorphism between them.

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