====== Image of a Group Homomorphism ======
====Definition==== 
Let $f:G\to H$ be a [[definition:group homomorphism]].  The $\textdef{image}$ of $f$ is the set of elements of $H$ that are mapped to by $f$, namely $$\im f = \{ f(g)\mid g\in G\}.$$


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==== Remarks ==== 
  * I would like to use Cryptography to help the students see that the image of a group homomorphism must always be a subgroup of $H$. 


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==== $\LaTeX$ version ====
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==== External links ====
  * [[wp>Group_homomorphism#Image_and_kernel]]


{{tag>definition ben needsreview rben rjosh}}