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Math Help - Is the image always a normal subgroup?

  1. #1
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    Is the image always a normal subgroup?

    There is a homomorphism between G and G'. Does the image of the homomorphism always give a normal subgroup?

    My thought is not always, because the homomorphism is not a bijective map. But how do I find a counterexample for this?
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  2. #2
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    As an easy example take f: Z_2 --> S_3, f(a):= (12) , where Z_2 = {1,a}.

    Tonio
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