IA-automorphisms of relatively free nilpotent torsion-free groups and Lie algebras

Abstract

For a free metabelian and nilpotent group G of finite rank n and class c, with and we show that for all and we extend this result to several torsion-free nilpotent varieties of groups. By our methods, which are based on a connection of automorphisms of groups with automorphisms of Lie algebras, we also show the analogous result for several relatively free nilpotent Lie algebras.