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PreprintarXiv licencearXiv

Torsion-freeness problem for matrix groups

  • Ruiwen Dong
  • Emmanuel Rauzy
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Abstract

We establish three results on decision problems for finitely generated matrix groups, based on fiber products: • The torsion-freeness problem is undecidable for subgroups of SL4(ℤ), • There exists a finitely generated subgroup G of SL4(ℤ) with undecidable square root problem, • No algorithm can, on input a tuple of invertible matrices, output the list of marked finite quotients of the group they generate.

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Cite

BibTeXRIS
BibTeX
@misc{dong2026torsionfreeness,
  title = {{Torsion-freeness problem for matrix groups}},
  author = {Ruiwen Dong and Emmanuel Rauzy},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15378},
  eprint = {2609.15378},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15378},
}
RIS
TY  - UNPB
TI  - Torsion-freeness problem for matrix groups
AU  - Ruiwen Dong
AU  - Emmanuel Rauzy
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15378
UR  - https://arxiv.org/abs/2609.15378
AB  - We establish three results on decision problems for finitely generated matrix groups, based on fiber products: • The torsion-freeness problem is undecidable for subgroups of SL_4(ℤ), • There exists a finitely generated subgroup G of SL_4(ℤ) with undecidable square root problem, • No algorithm can, on input a tuple of invertible matrices, output the list of marked finite quotients of the group they generate.
ER  -