Characterizing inner automorphisms of groups
P. E. Schupp has shown, using small cancellation theory, that the inner automorphisms of a group G are characterized by the fact that they extend to any group which contains G as a subgroup. Here we record an elementary proof of Schupp's result based on a graph construction and an associated group presentation. An advantage of this approach is that it yields also the dual result that the inner automorphisms of G are precisely those automorphisms which can be lifted to any group of which G is a homomorphic image. In addition, both characterizations are seen to apply within certain restricted classes of groups (such as the class of p- groups of a given infinite order). Much of the argument is devoted to establishing a general version of a well-known theorem of H. Heineken and H. Liebeck.
scientific article; zbMATH DE number 4118590