On sofic monoids
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.
Keywords
Cite
@article{arxiv.1304.4919,
title = {On sofic monoids},
author = {Tullio Ceccherini-Silberstein and Michel Coornaert},
journal= {arXiv preprint arXiv:1304.4919},
year = {2015}
}
Comments
We have corrected a small mistake in (and then suitably refrmulated) the statement of Theorem 6.1 (we needed the "Left-cancellative" hypothesis on M. It will appear in SEMIGRUOP FORUM