A Presentation of the Automorphism Group of the Two-Generator Free Metabelian and Nilpotent Group of Class $c$

Abstract

We determine the structure of IA(G)/Inn(G) by giving a set of generators, and showing that IA(G)/Inn(G) is a free abelian group of rank (c − 2)(c + 3)/2. Here G = M ₂, c = 〈 x, y〉, c ≥ 2, is the free metabelian nilpotent group of class c