Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911698263212032 |
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| author | Margolis, Stuart Rhodes, John |
| author_facet | Margolis, Stuart Rhodes, John |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19569 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1 Margolis, Stuart Rhodes, John Group Theory 20M10, 20M20, 20M30, 20M35 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. |
| title | Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1 |
| topic | Group Theory 20M10, 20M20, 20M30, 20M35 |
| url | https://arxiv.org/abs/2605.19569 |