Class-preserving automorphisms of groups

Let G be a group.  An automorphism of G is called class-preserving if it maps each group element to a conjugate of it.  The obvious examples of class-preserving automorphisms are inner automorphisms. The first example of a group having non-inner class-preserving automorphisms was given by Burnside in 1913.  In this talk we shall present a brief survey of the topic and discuss the nilpotency of the outer class-preserving automorphism group, i.e. the factor group Aut_c(G) / Inn(G), where Aut_c(G) is the group of class-preserving automorphisms of G.