A countable family of finitely presented infinite congruence-free monoids

2013/04/17 by Alan J. Cain, Cain, Alan J., Victor Maltcev +3
Computer Science · Mathematics · #20M05 (Primary) 20M10 (Secondary) #Advanced Combinatorial Mathematics #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20M05 #msc:20M10 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1304.4687

7 pages

arxiv created 2013/04/17 · openalex publication_date 2013/04/17 · arxiv updated 2013/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that monoids Mon⟨ a,b,c,d : aⁿb=0, ac=1, db=1, dc=1, dab=1, da²b=1, …, da^n-1b=1⟩ are congruence-free for all n≥ 1. This provides a new countable family of finitely presented congruence-free monoids, bringing one step closer to understanding the Boone--Higman Conjecture. We also provide examples which show that finitely presented congruence-free monoids may have quadratic Dehn function.

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