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image (of a homomorphism)

For a homomorphism $f: G \to H$ , the set $\operatorname{im}(f) = \{f(g) : g \in G\}$ -- always a subgroup of $H$ , though never automatically normal in $H$ .

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Examples

For the inclusion map $A_3\hookrightarrow S_3$ , the image is all of $A_3$ itself.