Question:Inner automorphisms preserving conjugacy classes
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.
Wiki read exploratory note: Here's how you could discover this answer through the wiki without using Questions:
- Go to the page on inner automorphism
- First note that none of the definitions of inner automorphism define it as an automorphism that preserves conjugacy classes.
- Next, scroll down to the inner automorphism#Weaker properties]] section and see there the listed property class-preserving automorphism with the correct Meaning as well as with links on the side to inner implies class-preserving and class-preserving not implies inner.