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In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.

In abstract algebra, a group isomorphism is a function between two groups that sets up a one-to-one correspondence between the elements of the groups in a way that respects the given group operations.

As an example, consider the groups $(\mathbb{R},+)$ and $\bigl((0,+\infty),\times\bigr)$. Then $\exp\colon\mathbb{R}\longrightarrow(0,+\infty)$ is an isomorphism.

If there exists an isomorphism between two groups, then the groups are called isomorphic. From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished.