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====== Group Isomorphism ======
====Definition==== 
Let $f:G\to H$ be a [[definition:group homomorphism|homomorphism]] of [[definition:group|groups]]. If $f$ is also a [[wp>bijection]], then we say that $f$ is a (group) $\textdef{isomorphism}$. If there exists an isomorphism between $G$ and $H$, then we say that $G$ and $H$ are $\textdef{isomorphic}$, denoted $G\cong H$.


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


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==== $\LaTeX$ version ====
<code>
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\begin{definition}
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\end{definition}
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==== External links ====
  * [[wp>Group isomorphism]]


{{tag>definition ben needsreview rben rjosh}}

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