Maximal normal subgroups of the automorphism groups of free nilpotent groups

Abstract

We prove that the subgroup of all IA-automorphisms of the automorphism group Aut(N) of a free nilpotent group N of infinite rank is normality-small. As a consequence, every maximal normal subgroup of the group Aut(N) is a lifting of a maximal normal subgroup of the automorphism group Aut(A) of the abelianization A = N/[N, N] of N.