Automorphisms of Aut(A),Aa Free Abelian Group

Abstract

We prove that all automorphisms of the automorphism group of an infinitely generated free abelian group are inner.

On the automorphism groups of relatively free groups of infinite rank: a survey

“…Note, that Inn(Aut(A ∞ )) = Aut(Aut(A ∞ )) ( [19], [20]). Anyway Aut(A ∞ ) is not complete because it contains a non-central the inverting authomorphism.…”