Uniform small cancellation in torsion-free hyperbolic groups

Olga Kharlampovich; Rizos Sklinos

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arXiv · 2610.11100

Uniform small cancellation in torsion-free hyperbolic groups

Olga Kharlampovich·Rizos Sklinos

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Abstract

We establish a uniform small cancellation theorem for non-elementary torsion-free hyperbolic groups: given any prescribed small cancellation constant, finitely many fixed words suffice to produce a small cancellation element from every pair of noncommuting elements. As an application, we prove that the first-order theory of every non-elementary torsion-free hyperbolic group does not admit a model companion.

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Olga Kharlampovich, Rizos Sklinos. 2026-10-08. Uniform small cancellation in torsion-free hyperbolic groups. https://arxiv.org/abs/2610.11100

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