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

Mallika Roy

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arXiv · 2607.08900

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

Mallika Roy

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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.

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Mallika Roy. 2026-07-09. Finitely presented kernels of right-angled Artin groups with abelian quotients. https://arxiv.org/abs/2607.08900

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