A conjecture for varieties of completely regular semigroups
Mario Petrich ยท Mathematica Slovaca ยท 2019
Abstract The class ๐โ of completely regular semigroups considered with the unary operation of inversion within maximal subgroups forms a variety. The B-relation on the lattice โ(๐โ) of subvarieties of ๐โ identifies two varieties if they contain the same bands. Its classes are intervals with the set ฮ of upper ends of these intervals. Canonical varieties form part of ฮ. Previously we determined the sublattice ฮจ of โ(๐โ) generated by the variety ๐๐ฎ of completely simple semigroups and six canonical varieties. The conjecture is that the sublattice of โ(๐โ) generated by ๐๐ฎ and canonical varieties follows the pattern of the structure of ฮจ.