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Subgroups of direct products of limit groups over Droms RAAGs

Jone Lopez de Gamiz Zearra

Algebraic & Geometric Topology 22 (2022) 3485–3510

A result of Bridson, Howie, Miller and Short states that if S is a subgroup of type FPn() of the direct product of n limit groups over free groups, then S is virtually the direct product of limit groups over free groups. Furthermore, they characterise finitely presented residually free groups. In this paper these results are generalised to limit groups over Droms right-angled Artin groups. Droms RAAGs are the right-angled Artin groups with the property that all of their finitely generated subgroups are again RAAGs. In addition, we show that the generalised conjugacy problem is solvable for finitely presented groups that are residually a Droms RAAG, and that their finitely presentable subgroups are separable.

homology of groups, limit groups over Droms RAAGs, residually Droms RAAGs
Mathematical Subject Classification
Primary: 20F65
Secondary: 20J05
Received: 18 October 2020
Revised: 3 September 2021
Accepted: 11 October 2021
Published: 30 January 2023
Jone Lopez de Gamiz Zearra
Mathematics Institute
University of Warwick
United Kingdom