On one-relator products induced by generalised triangle groups I

Ihechukwu Chinyere, James Howie

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1 Citation (Scopus)
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In this paper and a sequel, we study a group which is the quotient of a free oduct of groups by the normal closure of a single word that is contained in a subgroup which has the form of a free product of two cyclic groups.

We use known properties of generalised triangle groups, together with detailed analysis of pictures and of words in free monoids, to prove a number of results such as a Freiheitssatz and the existence of Mayer-Vietoris sequences for such groups under suitable hypotheses. The results eneralise those in an earlier article of the second author and Shwartz
Original languageEnglish
Pages (from-to)1138-1154
Number of pages16
JournalCommunications in Algebra
Issue number3
Early online date11 Aug 2017
Publication statusE-pub ahead of print - 11 Aug 2017


  • One-relator group
  • generalised triangle groups
  • Pictures

ASJC Scopus subject areas

  • General Mathematics


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