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.

Sources & referencesView supporting material

Primary source

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

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