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

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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 languageEnglish
Pages (from-to)698-735
Number of pages38
JournalJournal of Algebra
Volume635
DOIs
Publication statusPublished - 1 Dec 2023

Keywords

  • Group
  • Identity
  • Identity basis
  • Semigroup
  • Variety

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