Residual Finiteness of $A_{2,3,2n}$ Triangle Artin Groups

TL;DR

This paper proves that a specific class of triangle Artin groups, denoted as $A_{2,3,2n}$, are residually finite for all $n \, \geq 4$, by analyzing their structure as graphs of groups.

Contribution

It introduces a novel approach by splitting these Artin groups into graphs of groups and establishing finite stature to prove residual finiteness.

Findings

All $A_{2,3,2n}$ triangle Artin groups are residually finite for $n \geq 4$.

The groups can be decomposed into graphs of groups with finite stature.

The method applies to a broad class of Artin groups.

Abstract

We prove that triangle Artin groups of the type $A_{2,3,2n}$ are residually finite for all $n\geq4$. This requires splitting these triangle Artin groups as graphs of groups and then proving that each of these graphs of groups has finite stature with respect to its vertex groups.