Virtually special non-finitely presented groups via linear characters

Abstract

We present a new method for showing that groups are virtually special. This is done by considering finite quotients and linear characters. We use this to show that an infinite family of groups, related to Bestvina-Brady groups and branching, provides new examples of virtually special groups outside of a hyperbolic context.

Finitely generated groups acting uniformly properly on hyperbolic space

“…One should compare this to [15], where a similar construction is applied to generalised Bestvina-Brady groups. There it is shown that if H W is virtually torsion-free, then the set of relators for which p-th powers are taken has to be periodic.…”