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The Residual Finiteness of Triangle Artin Groups

Creative Commons 'BY' version 4.0 license
Abstract

We prove that all triangle Artin groups of the form $A_{2,3,2n}$ where $n>3$ are residually finite. To achieve this, we use the presentation for these groups previously employed by Wu and Ye to establish that each of them splits as a graph of groups. Building on techniques developed by Jankiewicz for other triangular subclasses of Artin groups, we adapt and extend these methods to show residual finiteness in this setting. Additionally, we developed a Python program to assist in specific computations for the case of $A_{2,3,8}$.

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