Rips construction without unique product

Abstract

Given a finitely presented group $Q,$ we produce a short exact sequence $1\to N\hookrightarrow G\twoheadrightarrow Q\to 1$ such that $G$ is a torsion-free Gromov hyperbolic group without the unique product property and $N$ is without the unique product property and has Kazhdan's Property (T). Varying $Q,$ we show a wide diversity of concrete examples of Gromov hyperbolic groups without the unique product property. As an application, we obtain Tarski monster groups without the unique product property.

22 pages

References in corpus (2)

• Rips-Segev torsion-free groups without the unique product property
• Finite index subgroups without unique product in graphical small cancellation groups

Cited by in corpus (4)

• A counterexample to the unit conjecture for group rings
• Finite index subgroups without unique product in graphical small cancellation groups
• Infinitely presented C(6)-groups are SQ-universal
• Subgroups of Lacunary Hyperbolic Groups and Free Products