Let $f:G\to H$ be a homomorphism. If $f$ is also a bijection, then we say that $f$ is a (group) isomorphism. If there exists an isomorphism between $G$ and $H$, then we say that $G$ and $H$ are isomorphic.

• Sometimes we may say that two groups are the same (or equal) when we mean that they are isomorphic.

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• http://en.wikipedia.org/wiki/Group_isomorphism

definition ben needsreview