The automorphism group of certain polycyclic groups
The automorphism group of certain polycyclic groups
For $\beta\in{\mathbb Z}$, let $G(\beta)=\langle A,B\,|\, A^{[A,B]}=A,\, B^{[B,A]}=B^\beta\rangle$ be the infinite Macdonald group, and set $C=[A,B]$. Then $G(\beta)$ is a nilpotent polycyclic group of the form $\langle A\rangle\ltimes\langle B,C\rangle$, where $A$ has infinite order. If $\beta\neq 1$, then $G(\beta)$ is of class 3 and $\langle B,C\rangle$ is a finite metacyclic …