Finite semigroups embed in finitely presented congruence-free monoids

TL;DR

This paper demonstrates that any finite semigroup can be embedded into a finitely presented congruence-free monoid, advancing understanding of algebraic structures and their embeddings.

Contribution

It establishes the embedding of all finite semigroups into finitely presented congruence-free monoids, providing new insights into algebraic structure theory.

Findings

Every finite semigroup embeds in a finitely presented congruence-free monoid

Raises questions related to the Boone-Higman Conjecture

Contributes to the theory of algebraic embeddings

Abstract

We prove that every finite semigroup embeds in a finitely presented congruence-free monoid, and pose some questions around the Boone-Higman Conjecture.