Equidivisible pseudovarieties of semigroups

@article{Almeida2016EquidivisiblePO,
  title={Equidivisible pseudovarieties of semigroups},
  author={Jorge Almeida and Alfredo Costa},
  journal={Publicationes Mathematicae Debrecen},
  year={2016},
  volume={90},
  pages={435-453}
}
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… 
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