Question:Inner automorphisms preserving conjugacy classes

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This question is about inner automorphism | See more questions about inner automorphism

Question: An inner automorphism sends every element to within its conjugacy class. Are there outer automorphisms that do so?

Answer: Yes. An automorphism that sends every element to within its conjugacy class is a class-preserving automorphism. See inner implies class-preserving, class-preserving not implies inner, and group in which every class-preserving automorphism is inner.

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