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A semilattice of varieties of completely regular semigroups

Mario Petrich (2020)

Mathematica Bohemica

Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by ( 𝒞 ) . We construct a 60-element -subsemilattice and a 38-element sublattice of ( 𝒞 ) . The bulk of the paper consists in establishing the necessary joins for which it uses Polák’s theorem.

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