Splittings of triangle Artin groups

Abstract

We show that a triangle Artin group ${\mathrm{Art}}_{MNP}$, where $M\le N\le P$, splits as an amalgamated product or an HNN extension of finite rank free groups, provided that either $M>2$ or $N>3$. We also prove that all even 3-generator Artin groups are residually finite.