I have a question about Automorphisms. Please check the following statement for validity....(adsbygoogle = window.adsbygoogle || []).push({});

An automorphism of a group should map generators to generators. Suppose it didn't, well then the group structure wouldn't be preserved and since automorphisms are homomorphisms this would be a contradiction.

If this is valid is there an example of a homomorphism (not an automorphism) of groups, say ##\phi:G\to H## that doesn't map a generator of ##G## to a generator of ##H##?

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# Abstract Algebra: Automorphisms

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