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arXiv · 1407.2441

Rips construction without unique product

Goulnara Arzhantseva·Markus Steenbock
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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.

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Goulnara Arzhantseva, Markus Steenbock. 2014-07-09. Rips construction without unique product. https://doi.org/10.2140/pjm.2023.322.1

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