A study of the Wamsley group and its Sylow subgroups

Abstract

We study the Wamsley group $⟨X,Y,Z|X^Z=X^{\alpha },{}^{Z}Y=Y^{\beta },Z^{\gamma }=[X,Y]⟩$ and its Sylow subgroups, where ${\alpha }^{\gamma }\ne 1\ne {\beta }^{\gamma }$ and $\gamma >0$, obtaining the sharpest results when $\alpha =\beta$.