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 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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DOI:
https://doi.org/10.1090/S0002-9939-1988-0920981-1

Keywords:
Freiheitssatz,
one-relator product,
generalized triangle group

Article copyright:
© Copyright 1988
American Mathematical Society