English

Subgroup Separability of Artin Groups II

Group Theory 2024-03-11 v1

Abstract

In this paper, we establish a new criterion for determining whether an Artin group is subgroup separable (LERF), building upon a criterion introduced in a previous work. Specifically, we prove an Artin group is LERF if and only if it does not contain certain induced subgraphs, thus providing a more direct generalization of the Metaftsis-Raptis criterion for RAAGs. As consequences, we prove an Artin group is ERF if and only if it is a free abelian group and we establish a link between subgroup separability and coherence for Artin groups.

Cite

@article{arxiv.2403.05483,
  title  = {Subgroup Separability of Artin Groups II},
  author = {Kisnney Almeida and Igor Lima},
  journal= {arXiv preprint arXiv:2403.05483},
  year   = {2024}
}
R2 v1 2026-06-28T15:13:52.019Z