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arXiv · 2605.19569

Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1

Stuart Margolis·John Rhodes
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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 S^{Ev} . We use the theory of flows to show that a group mapping semigroup S admits an aperiodic flow if and only if S^{Ev} admits one. This reduces the computation of Krohn-Rhodes complexity 1 to the class of smallish monoids.

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Stuart Margolis, John Rhodes. 2026-05-19. Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1. https://arxiv.org/abs/2605.19569

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