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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{kharlampovich2026uniform,
  title = {{Uniform small cancellation in torsion-free hyperbolic groups}},
  author = {Olga Kharlampovich and Rizos Sklinos},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.11100},
  eprint = {2610.11100},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.11100},
}
RIS
TY  - UNPB
TI  - Uniform small cancellation in torsion-free hyperbolic groups
AU  - Olga Kharlampovich
AU  - Rizos Sklinos
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.11100
UR  - https://arxiv.org/abs/2610.11100
AB  - 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.
ER  -