Around subgroups of Artin groups: derived subgroups and acylindrical hyperbolicity in the even FC-case

Lopez de Gamiz Zearra, Jone; Martínez-Pérez, Conchita

doi:10.2140/agt.2026.26.2475

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Around subgroups of Artin groups: derived subgroups and acylindrical hyperbolicity in the even FC-case

Jone Lopez de Gamiz Zearra and Conchita Martínez-Pérez

Algebraic & Geometric Topology 26 (2026) 2475–2496

DOI: 10.2140/agt.2026.26.2475

Abstract

We generalize to (certain) Artin groups some results previously known for right-angled Artin groups (RAAGs). First, we generalize a result by Droms, B. Servatius, and H. Servatius, and prove that the derived subgroup of an Artin group is free if and only if the group is coherent. Second, coherent Artin groups over noncomplete graphs split as free amalgamated products along free abelian subgroups, and we extend to arbitrary Artin groups admitting such a splitting a recent result by Casals-Ruiz and Lopez de Gamiz Zearra on finitely generated normal subgroups of RAAGs. Finally, we use splittings of even Artin groups of FC-type to generalize results of Minasyan and Osin on acylindrical hyperbolicity of their subgroups.

Keywords

Artin groups, normal subgroups

Mathematical Subject Classification

Primary: 20F36, 20F65

Secondary: 20E07, 20E08

References

Publication

Received: 13 June 2024

Revised: 26 April 2025

Accepted: 21 June 2025

Published: 1 September 2026

Authors

Jone Lopez de Gamiz Zearra
Métodos cuantitativos, Facultad de Economía y Empresa University of the Basque Country EHU/UPV Bilbao Spain

Conchita Martínez-Pérez
Departamento de Matemáticas Universidad de Zaragoza Zaragoza Spain

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Volume 26, issue 7 (2026)