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Random groups are not left-orderable

Volume 150 / 2017

Damian Orlef Colloquium Mathematicum 150 (2017), 175-185 MSC: Primary 20F65; Secondary 20F60. DOI: 10.4064/cm7074-11-2016 Published online: 17 July 2017


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.


  • Damian OrlefInstitute of Mathematics
    Polish Academy of Sciences
    00-656 Warszawa, Poland

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