A large class of sofic monoids

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We prove that a monoid is sofic, in the sense recently introduced by Ceccherini-Silberstein and Coornaert, whenever the J-class of the identity is a sofic group, and the quotients of this group by orbit stabilisers in the rest of the monoid are amenable. In particular, this shows that the following are all sofic: left or right cancellative monoids with amenable group of units; monoids with sofic group of units and finitely many non-units; and monoids with amenable Schützenberger groups and finitely many L-classes in each D-class. This provides a very wide range of sofic monoids, subsuming most known examples (with the notable exception of locally residually finite monoids). We conclude by discussing some aspects of the definition, and posing some questions for future research.

Original languageEnglish
Pages (from-to)282-294
Number of pages13
JournalSemigroup Forum
Issue number1
Early online date3 Jul 2015
Publication statusPublished - 26 Aug 2015


  • Amenable group
  • Schützenberger group
  • Sofic monoid


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