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

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

http://hdl.handle.net/10362/165334

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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.