On sofic monoids |
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Authors: | Tullio Ceccherini-Silberstein Michel Coornaert |
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Institution: | 1. Dipartimento di Ingegneria, Università del Sannio, C.so Garibaldi 107, Benevento, 82100, Italy 2. Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René-Descartes, Strasbourg, 67000, France
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Abstract: | We investigate a notion of soficity for monoids. A group is sofic as a group if and only if it is sofic as a monoid. All finite monoids, all commutative monoids, all free monoids, all cancellative one-sided amenable monoids, all multiplicative monoids of matrices over a field, and all monoids obtained by adjoining an identity element to a semigroup are sofic. On the other hand, although the question of the existence of a non-sofic group remains open, we prove that the bicyclic monoid is not sofic. This shows that there exist finitely presented amenable inverse monoids that are non-sofic. |
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