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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0920981-1
PII: S 0002-9939(1988)0920981-1
Keywords: Freiheitssatz, one-relator product, generalized triangle group
Article copyright: © Copyright 1988 American Mathematical Society