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Proceedings of the American Mathematical Society

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One-relator quotients and free products of cyclics

Authors: Benjamin Fine, James Howie and Gerhard Rosenberger
Journal: Proc. Amer. Math. Soc. 102 (1988), 249-254
MSC: Primary 20F05,; Secondary 20E06
MathSciNet review: 920981
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Abstract: It is proven that the Freiheitssatz holds for all one-relator products of cyclic groups if the relator is cyclically reduced and a proper power. The method of proof involves representing such groups in $ {\text{PS}}{{\text{L}}_2}({\mathbf{C}})$ and is a refinement of a technique of Baumslag, Morgan and Shalen. The technique allows the extension of the Freiheitssatz result to many additional one-relator products.

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Keywords: Freiheitssatz, one-relator product, generalized triangle group
Article copyright: © Copyright 1988 American Mathematical Society

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