A survey on varieties generated by small semigroups and a companion website

João Araújo; João Pedro Araújo; Peter J. Cameron; Edmond W. H. Lee; Jorge Raminhos

doi:10.1016/j.jalgebra.2023.06.030

A survey on varieties generated by small semigroups and a companion website

João Araújo^*, João Pedro Araújo, Peter J. Cameron, Edmond W. H. Lee, Jorge Raminhos

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents new findings on varieties generated by small semigroups and groups, and offers a survey of existing results. A companion website is provided which hosts a computational system integrating automated reasoning tools, finite model builders, SAT solvers, and GAP. This platform is a living guide to the literature. In addition, the first complete and justified list of identity bases for all varieties generated by a semigroup of order up to 4 is provided as supplementary material. The paper concludes with an extensive list of open problems and conjectures.

Original language	English
Pages (from-to)	698-735
Number of pages	38
Journal	Journal of Algebra
Volume	635
Early online date	15 Sept 2023
DOIs	https://doi.org/10.1016/j.jalgebra.2023.06.030
Publication status	Published - 1 Dec 2023

Keywords

Semigroups
Varietes

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10.1016/j.jalgebra.2023.06.030Licence: CC BY-NC

Araujo_2023_JoA_Survey-varieties_CC
Copyright © 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Final published version, 1.6 MBLicence: CC BY-NC

Cite this

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AU - Araújo, João Pedro

AU - Cameron, Peter J.

AU - Lee, Edmond W. H.

AU - Raminhos, Jorge

PY - 2023/12/1

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AB - This paper presents new findings on varieties generated by small semigroups and groups, and offers a survey of existing results. A companion website is provided which hosts a computational system integrating automated reasoning tools, finite model builders, SAT solvers, and GAP. This platform is a living guide to the literature. In addition, the first complete and justified list of identity bases for all varieties generated by a semigroup of order up to 4 is provided as supplementary material. The paper concludes with an extensive list of open problems and conjectures.

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KW - Varietes

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DO - 10.1016/j.jalgebra.2023.06.030

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

A survey on varieties generated by small semigroups and a companion website

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Keywords

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