On singular equations over torsion-free groups

Martin Edjvet, James Howie*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We prove a Freiheitssatz for one-relator products of torsion-free groups, where the relator has syllable length at most 8. This result has applications to equations over torsion-free groups: in particular a singular equation of syllable length at most 18 over a torsion-free group has a solution in some overgroup.

Original languageEnglish
Pages (from-to)551-580
Number of pages30
JournalInternational Journal of Algebra and Computation
Issue number3
Early online date14 Apr 2021
Publication statusPublished - May 2021


  • Equations over groups
  • One-relator products

ASJC Scopus subject areas

  • General Mathematics


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