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arXiv · 1304.4919

On sofic monoids

Tullio Ceccherini-Silberstein·Michel Coornaert
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Abstract

We investigate the 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 without identity element 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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Tullio Ceccherini-Silberstein, Michel Coornaert. 2013-04-17. On sofic monoids. https://arxiv.org/abs/1304.4919

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