Dyer groups: Centres, hyperbolicity, and acylindrical hyperbolicity

Abstract

In this article we describe the centres of all Dyer groups. We also give a complete classification of when a Dyer group $D(\hat{I}“)$ is hyperbolic or acylindricality hyperbolic, with conditions that can easily be read on the Dyer graph $\hat{I}“$.

10 pages, 3 figures