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

Department of Mathematics

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.

Original language	American English
Pages (from-to)	698–735
Journal	Journal of Algebra
Volume	635
DOIs	https://doi.org/10.1016/j.jalgebra.2023.06.030
State	Published - Dec 1 2023

Funding

Supported by the Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications).Supported by the Fundação para a Ciência e a Tecnologia, I.P., through project CEMAT-Ciências UID/Multi/04621/2013.

Funders	Funder number
Fundação para a Ciência e a Tecnologia	UIDB/00297/2020, CEMAT-Ciências UID/Multi/04621/2013, UIDP/00297/2020
Fundação para a Ciência e a Tecnologia

ASJC Scopus Subject Areas

Algebra and Number Theory

Keywords

Variety
Semigroup
Group
Identity
Identity basis

Disciplines

Algebra
Mathematics

Access to Document

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

A survey on varieties generated by small semigroups and a companiFinal published version, 1.67 MBLicense: Unspecified

Cite this

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AU - Raminhos, Jorge

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

Abstract

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

Access to Document

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