Is the reason why the homomorphism is defined the way it is so that we can be sure that the image is a group?(adsbygoogle = window.adsbygoogle || []).push({});

Could you get a map which is not a homomorphism but still have the image as a group? This question is equivalent to asking whether in the domain group, elements can multiply differently so that it can still form a group. Can it?

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# Why is a homomorphism the way it is?

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