Random groups are not left-orderable
Volume 150 / 2017
Colloquium Mathematicum 150 (2017), 175-185
MSC: Primary 20F65; Secondary 20F60.
DOI: 10.4064/cm7074-11-2016
Published online: 17 July 2017
Abstract
We prove that random groups in the Gromov density model at any density $d$ have with overwhelming probability no non-trivial left-orderable quotients. In particular, random groups at densities $d \lt 1/2$ are not left-orderable.
