Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rips construction without unique product   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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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: alg-geom