A Countable Family of Finitely Presented Infinite Congruence-free Monoids
نویسندگان
چکیده
We prove that monoids Mon〈a, b, c, d : ab = 0, ac = 1, db = 1, dc = 1 dab = 1, dab = 1, . . . , dab = 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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