A countable family of finitely presented infinite congruence-free monoids

Fatma Al-Kharousi, Alan J. Cain, Victor Maltcev, Abdullahi Umar

Research output: Contribution to journalArticle


We prove that the monoids Monha, b, c, d: anb = 0, ac = 1, db = 1, dc = 1, dab = 1, da 2 b = 1,.., dan-1 b = 1i are congruence-free for all n = 1. This provides a new countable family of finitely presented congruence-free monoids, bringing us one step closer to understanding the monoid version of the Boone-Higman Conjecture. We also provide examples showing that finitely presented congruence-free monoids may have quadratic Dehn function.

Original languageEnglish
Pages (from-to)437-445
Number of pages9
JournalActa Scientiarum Mathematicarum
Issue number3-4
Publication statusPublished - 2015



  • Boone-Higman Conjecture
  • Congruence-free
  • Finitely presented
  • Rewriting systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this