Structure of the Macdonald groups in one parameter

Alexander Montoya Ocampo, Fernando Szechtman

Consider the Macdonald groups $G(\alpha )=⟨A,B|A^{[A,B]}=A^{\alpha },B^{[B,A]}=B^{\alpha }⟩$, $\alpha \in \mathbf{Z}$. We fill a gap in Macdonald's proof that $G(\alpha )$ is always nilpotent,…