Question:Inner automorphisms preserving conjugacy classes

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 answer references::class-preserving automorphism. See answer references::inner implies class-preserving, answer references::class-preserving not implies inner, and answer references::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.