Subgroup Separability of Artin Groups II

2024/03/08 by Kisnney Almeida, Almeida, Kisnney, Igor Gabriel Lima +1
Medicine · Mathematics · Physics and Astronomy · #Monoclonal and Polyclonal Antibodies Research #Geometric and Algebraic Topology #Force Microscopy Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2403.05483

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.

Related

• Subgroup Separability of Artin Groups
• Around subgroups of Artin groups: derived subgroups and acylindrical hyperbolicity in the even FC-case
• Conjugacy p-separability of right-angled Artin groups and applications
• On Subgroup Separability and Membership Problems in Twisted Right-Angled Artin Groups
• The submonoid and rational subset membership problems for Artin groups