Class-inner automorphism

From Groupprops
Jump to: navigation, search
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)
View other automorphism properties OR View other function properties

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


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

Relation with other properties

Stronger properties

Weaker properties