Torsion conjecture for virtual Artin groups

Let Γ\Gamma be a Coxeter graph, let VA[Γ]\mathrm{VA}[\Gamma] be the associated virtual Artin group, and let ιW(W[Γ])\iota_{\mathrm{W}}(\mathrm{W}[\Gamma]) denote its embedded copy of the associated Coxeter group. Torsion conjecture for virtual Artin groups. Every finite subgroup of VA[Γ]\mathrm{VA}[\Gamma] is conjugated into a subgroup of ιW(W[Γ])\iota_{\mathrm{W}}(\mathrm{W}[\Gamma]). This is unknown even for virtual braid groups, but is proved in the paper for locally reducible Coxeter graphs.

References

Primary source

Federica Gavazzi and Alexandre Martin, “A Deligne complex for virtual Artin groups”, arXiv:2607.24367 (2026).

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