Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1
Abstract
A smallish monoid M is a monoid that has a unique 0-minimal ideal I(M) that is a 0-simple subsemigroup and such that its regular J -classes are the group of units and the two in I(M). We show constructively how to embed an arbitrary finite semigroup S into the evaluation semigroup of a smallish monoid SEv . We use the theory of flows to show that a group mapping semigroup S admits an aperiodic flow if and only if SEv admits one. This reduces the computation of Krohn-Rhodes complexity 1 to the class of smallish monoids.
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