One-relator products induced from generalized triangle groups

James Howie, Robert Shwartz

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)2505-2526
Number of pages22
JournalCommunications in Algebra
Issue number7
Publication statusPublished - 2004


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


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