Hyperbolic groups of Fibonacci type and T(5) cyclically presented groups

Abstract

Building on previous results concerning hyperbolicity of groups of Fibonacci type, we give an almost complete classification of the (non-elementary) hyperbolic groups within this class. We are unable to determine the hyperbolicity status of precisely two groups, namely the Gilbert-Howie groups H(9, 4), H(9, 7). We show that if H(9, 4) is torsion-free then it is not hyperbolic. We consider the class of T(5) cyclically presented groups and classify the (non-elementary) hyperbolic groups and show that the Tits alternative holds.

Perfect Prishchepov groups

“…Cyclically presented groups have been an object of various investigations not just from the algebraic point of view as in [3,19,1,14,38,10,13] for example, but also from topological perspectives due to their connections with the topology of closed orientable 3-manifolds (see for example, [36,9,8,35,12,7,26]). In this article we take the former point of view.…”