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Preprint Number 1366

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1366. Simon André (IRMAR)
Hyperbolicity and Cubulability Are Preserved Under Elementary Equivalence
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Submission date: 29 January 2018

Abstract:

The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated group G has the same first-order theory as a group possessing one of the previous property, then G enjoys this property as well.

Mathematics Subject Classification:

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Full text arXiv 1801.09411: pdf, ps.


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