# Class-inner automorphism

From Groupprops

This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)

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BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Symbol-free definition

An automorphism of a group is said to be **class-inner** if, given any conjugacy class in the group:

- The automorphism maps the conjugacy class to itself
- There exists an inner automorphism of the whole group, whose restriction to that conjugacy class is the same as the restriction of the given automorphism