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Full-Text Articles in Physical Sciences and Mathematics
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
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
Mathematics Faculty Articles
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.