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Spherical and affine Artin groups, finite quotients, and the isomorphism problem

  • Sam Hughes
  • Thomas Ng
  • Kaitlin Ragosta
  • Nancy Scherich
  • Yvon Verberne
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Abstract

We compute the smallest non-abelian quotients of spherical and affine Artin groups. Usually, these are isomorphic to the smallest non-abelian quotients of the corresponding Coxeter groups. As applications, we deduce that two affine Artin groups are isomorphic if and only if their Coxeter diagrams are isomorphic and that irreducible spherical Artin groups are distinguished from each other by their finite quotient groups.

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Cite

BibTeXRIS
BibTeX
@misc{hughes2026spherical,
  title = {{Spherical and affine Artin groups, finite quotients, and the isomorphism problem}},
  author = {Sam Hughes and Thomas Ng and Kaitlin Ragosta and Nancy Scherich and Yvon Verberne},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.27171},
  eprint = {2609.27171},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27171},
}
RIS
TY  - UNPB
TI  - Spherical and affine Artin groups, finite quotients, and the isomorphism problem
AU  - Sam Hughes
AU  - Thomas Ng
AU  - Kaitlin Ragosta
AU  - Nancy Scherich
AU  - Yvon Verberne
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27171
UR  - https://arxiv.org/abs/2609.27171
AB  - We compute the smallest non-abelian quotients of spherical and affine Artin groups. Usually, these are isomorphic to the smallest non-abelian quotients of the corresponding Coxeter groups. As applications, we deduce that two affine Artin groups are isomorphic if and only if their Coxeter diagrams are isomorphic and that irreducible spherical Artin groups are distinguished from each other by their finite quotient groups.
ER  -