The automorphism group of certain polycyclic groups

Khalid Benabdallah, Agustin D'Alessandro, Fernando Szechtman

For $\beta \in \mathbb{Z}$, let $G(\beta )=⟨A,B|A^{[A,B]}=A,B^{[B,A]}=B^{\beta }⟩$ be the infinite Macdonald group, and set $C=[A,B]$. Then $G(\beta )$ is a nilpotent polycyclic gro…