Thu, 21 Mar 2024, 11:00 am MDT
We exhibit several finite monoids each of which is not contained in any variety generated by a finitely based finite semigroup but is contained in a finitely based locally finite variety. The smallest monoid with these properties we found so far has as few as 9 elements. The result solves a 20+ years old problem and has numerous implications for the finite basis problem for finite semigroups. This is joint work with Sergey Gusev (Ekaterinburg, Russia) and Olga Sapir (Beersheba, Israel)