Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1
Group Theory
2026-05-20 v1
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.
Keywords
Cite
@article{arxiv.2605.19569,
title = {Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1},
author = {Stuart Margolis and John Rhodes},
journal= {arXiv preprint arXiv:2605.19569},
year = {2026}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2501.18300