Krohn-Rhodes complexity pseudovarieties are not finitely based
Department of Mathematics,
University of California at Berkeley, Berkeley, CA 94720, USA;
2 School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada; firstname.lastname@example.org
We prove that the pseudovariety of monoids of Krohn-Rhodes complexity at most n is not finitely based for all n>0. More specifically, for each pair of positive integers n,k, we construct a monoid of complexity n+1, all of whose k-generated submonoids have complexity at most n.
Mathematics Subject Classification: 20M07
Key words: Complexity / finite basis problem / the presentation lemma
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