Subgroups of direct products of limit groups over Droms RAAGs

Lopez de Gamiz Zearra, Jone

doi:10.2140/agt.2022.22.3485

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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

DOI: 10.2140/agt.2022.22.3485

Abstract

A result of Bridson, Howie, Miller and Short states that if $S$ is a subgroup of type $F P_{n} (ℚ)$ 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.

Keywords

homology of groups, limit groups over Droms RAAGs, residually Droms RAAGs

Mathematical Subject Classification

Primary: 20F65

Secondary: 20J05

References

Publication

Received: 18 October 2020

Revised: 3 September 2021

Accepted: 11 October 2021

Published: 30 January 2023

Authors

Jone Lopez de Gamiz Zearra
Mathematics Institute University of Warwick Coventry United Kingdom
https://warwick.ac.uk/fac/sci/maths/people/staff/lopezdegamiz/

Volume 22, issue 7 (2022)