Equidivisible pseudovarieties of semigroups

TitleEquidivisible pseudovarieties of semigroups
Publication TypePreprint
Year of Preprint2016
AuthorsAlmeida J, Costa A

  We give a complete characterization of pseudovarieties of semigroups
  whose finitely generated relatively free profinite semigroups are
  equidivisible. Besides the pseudovarieties of completely simple
  semigroups, they are precisely the pseudovarieties that are closed
  under Mal'cev product on the left by the pseudovariety of locally
  trivial semigroups. A further characterization which turns out to be
  instrumental is as the non-completely simple pseudovarieties that
  are closed under two-sided Karnofsky-Rhodes expansion.