On certain 3-generator Artin groups

Squier, Craig C.

doi:10.1090/S0002-9947-1987-0887500-3

On certain $3$-generator Artin groups
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by Craig C. Squier

Trans. Amer. Math. Soc. 302 (1987), 117-124

DOI: https://doi.org/10.1090/S0002-9947-1987-0887500-3

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Abstract:

We describe the three $3$-generator Artin groups that correspond to the three sets $\{ p,q,r\}$ of positive integer solutions of ${p^{ - 1}} + {q^{ - 1}} + {r^{ - 1}} = 1$. In each case, we show that the Artin group is a free product with amalgamation or HNN extension involving finitely generated free groups and subgroups of finite index.

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