Mathematics Faculty Articles
Document Type
Article
Publication Date
12-1-2023
Publication Title
Journal of Algebra
Keywords
Variety, Semigroup, Group, Identity, Identity basis
ISSN
0021-8693
Volume
635
First Page
698
Last Page
735
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.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
NSUWorks Citation
Araújo, João; Araújo, João Pedro; Cameron, Peter J.; Lee, Edmond W. H.; and Raminhos, Jorge, "A survey on varieties generated by small semigroups and a companion website" (2023). Mathematics Faculty Articles. 360.
https://nsuworks.nova.edu/math_facarticles/360
ORCID ID
0000-0002-1662-3734
DOI
10.1016/j.jalgebra.2023.06.030
Comments
Appendix A. Supplementary material
The following is the Supplementary material related to this article.
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