Random groups do not have Property (T) at densities below 1/4

2022/06/29 by Calum J. Ashcroft, Ashcroft, Calum J
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2206.14616

openalex publication_date 2022/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that random groups in the Gromov density model at density d <1/4 do not have Property (T), answering a conjecture of Przytycki. We also prove similar results in the k-angular model of random groups.

Related

• Property (T) in density-type models of random groups
• Random groups are not left-orderable
• Cubulating random groups in the square model
• Property (T) in k-gonal random groups
• Linear representations of random groups