Finitely presented kernels of right-angled Artin groups with abelian quotients

Mallika Roy

Finitely presented kernels of right-angled Artin groups with abelian quotients

Group Theory 2026-07-09 v1

Authors: Mallika Roy

Abstract

In this article, we characterise when the kernels of right-angled Artin groups with abelian quotients are finitely generated and finitely presented -- exhibiting an explicit finite generating set and finite presentation. As an application, we deduce the finite presentation of the kernel of any character of a right-angled Artin group. These results generalise the presentation of the kernel of a rational character of a right-angled Artin group given by Casals--Kazachkov--Roy and Dicks and Leary's presentations of Bestina--Brady groups.

Keywords

right-angled Artin groups kernels abelian quotients finite generation finite presentation characters

Cite

@article{arxiv.2607.08900,
  title  = {Finitely presented kernels of right-angled Artin groups with abelian quotients},
  author = {Mallika Roy},
  journal= {arXiv preprint arXiv:2607.08900},
  year   = {2026}
}