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 · Journal of Algebra · 2023
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.