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

• 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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• http://en.wikipedia.org/wiki/Group_homomorphism#Image_and_kernel

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