A lattice of quasivarieties of normal cryptogroups. (Q2460066)

A normal cryptogroup \(S\) is a completely regular semigroup in which \(\mathcal H\) is a congruence and \(S/\mathcal H\) is a normal band. Such semigroups are also termed normal bands of groups. The lattice of varieties of normal cryptogroups was determined by the author (modulo, of course, varieties of groups) [Can. J. Math. 29, 1171-1197 (1977; Zbl 0342.20029)]. In the same paper, the quasivarieties of \(E\)-unitary normal cryptogroups (in fact of all \(E\)-unitary cryptogroups) were also determined, modulo quasivarieties of groups. Thus, as the author suggests, ``one is tempted to try to determine the lattice of all quasivarieties of normal cryptogroups''. While this goal is not achieved here, the author does describe the sublattice generated by the quasivarieties of normal bands, the variety of groups and the variety of completely simple semigroups.