One-relator quotients and free products of cyclics

Fine, Benjamin; Howie, James; Rosenberger, Gerhard

doi:10.1090/S0002-9939-1988-0920981-1

One-relator quotients and free products of cyclics
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by Benjamin Fine, James Howie and Gerhard Rosenberger PDF

Proc. Amer. Math. Soc. 102 (1988), 249-254 Request permission

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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