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Krohn-Rhodes complexity pseudovarieties are not finitely based

  • John Rhodes (a1) and Benjamin Steinberg (a2)


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.



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