The superstability conjecture for Artin groups

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An Artin group is a group defined by an Artin presentation; a group is superstable when its first-order theory has the model-theoretic superstability property.

Superstability conjecture. An Artin group is superstable if and only if it is abelian.

Superstability has strong structural consequences, while non-abelian free groups are not superstable. The source proves non-superstability for non-abelian Artin groups in several classes, including spherical, large, and even FC type, but the assertion for all Artin groups remains open.

References

Primary source

Alberto Cassella, Gianluca Paolini and Giovanni Paolini, “First-order aspects of Artin groups”, arXiv:2507.21575 (2025).

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