A sixteen-relator presentation of an infinite hyperbolic Kazhdan group

Abstract

We provide an explicit presentation of an infinite hyperbolic Kazhdan group with 4 generators and 16 relators of length at most 73. That group acts properly and cocompactly on a hyperbolic triangle building of type (3, 4, 4). We also point out a variation of the construction that yields examples of lattices in ${\tilde{A}}_2$-buildings admitting non-Desarguesian residues of arbitrary prime power order.