Work

The submonoid and rational subset membership problems for Artin groups

Year: 2026

Type: article

Abstract: We demonstrate that the submonoid membership problem and the rational subset membership problem are equivalent in Artin groups. Both problems are undecidable in a given Artin group if and only if the group embeds the right-angled Artin groups of rank 4 over a path or a square; and this can be characterized using only the defining graph of the Artin group. These results generalize those of Lohrey - Steinberg for right-angled Artin groups. Moreover, both decision problems are decidable for a given Artin group if and only if the group is subgroup separable.

Source: Journal of Algebra

DOI: 10.1016/j.jalgebra.2026.02.029

Author: Islam Foniqi

Institution: University of East Anglia

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,310

Funder: Engineering and Physical Sciences Research Council