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arXiv · 2403.05483

Subgroup Separability of Artin Groups II

Kisnney Almeida·Igor Lima
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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.

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Kisnney Almeida, Igor Lima. 2024-03-08. Subgroup Separability of Artin Groups II. https://arxiv.org/abs/2403.05483

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