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PreprintCC BY-NC-ND 4.0HAL

Smallest quotients and profinite rigidity of irreducible spherical type Artin groups

  • Federica Gavazzi
  • Igor Haladjian
  • Luis Paris
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Abstract

We prove that irreducible spherical type Artin groups are profinitely rigid within the class of all spherical type Artin groups. As part of the proof, building on ideas of Kolay for the n-strand braid group, we compute the smallest non-abelian quotient of every spherical type Artin group. In particular, given an irreducible spherical type Artin group, its smallest non-abelian quotient is always that of the corresponding Coxeter group, except for dihedral Artin groups of weight divisible by 4, which all have S3 as a non-abelian quotient. Parts of the proof also rely on the computation of the cohomological dimension of the profinite completion of certain Artin groups

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Cite

BibTeXRIS
BibTeX
@misc{gavazzi2026smallest,
  title = {{Smallest quotients and profinite rigidity of irreducible spherical type Artin groups}},
  author = {Federica Gavazzi and Igor Haladjian and Luis Paris},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25940},
  eprint = {2609.25940},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05757814v1},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Smallest quotients and profinite rigidity of irreducible spherical type Artin groups
AU  - Federica Gavazzi
AU  - Igor Haladjian
AU  - Luis Paris
PY  - 2026
DA  - 2026/09/18
PB  - HAL
DO  - 10.48550/arxiv.2609.25940
UR  - https://hal.science/hal-05757814v1
AB  - We prove that irreducible spherical type Artin groups are profinitely rigid within the class of all spherical type Artin groups. As part of the proof, building on ideas of Kolay for the n-strand braid group, we compute the smallest non-abelian quotient of every spherical type Artin group. In particular, given an irreducible spherical type Artin group, its smallest non-abelian quotient is always that of the corresponding Coxeter group, except for dihedral Artin groups of weight divisible by 4, which all have S_3 as a non-abelian quotient. Parts of the proof also rely on the computation of the cohomological dimension of the profinite completion of certain Artin groups
ER  -