### Abstract

We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a pushout involving a generalized triangle group. Using the theory of generalized triangle groups, we extend the range of conditions under which a number of results for one-relator products of groups, such as the Freiheitssatz and the solubility of the word problem, are known to hold. Copyright © 2004 by Marcel Dekker, Inc.

Original language | English |
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Pages (from-to) | 2505-2526 |

Number of pages | 22 |

Journal | Communications in Algebra |

Volume | 32 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2004 |

### Keywords

- Freiheitssatz
- Generalized triangle group
- One-relator
- Word problem

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## Cite this

Howie, J., & Shwartz, R. (2004). One-relator products induced from generalized triangle groups.

*Communications in Algebra*,*32*(7), 2505-2526. https://doi.org/10.1081/AGB-120037396