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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

On certain $ 3$-generator Artin groups


Author: Craig C. Squier
Journal: Trans. Amer. Math. Soc. 302 (1987), 117-124
MSC: Primary 20F05; Secondary 20E06, 20F36
MathSciNet review: 887500
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0887500-3
PII: S 0002-9947(1987)0887500-3
Article copyright: © Copyright 1987 American Mathematical Society