An infinite order operator on the lattice of varieties of completely regular semigroups (Q1921398)

This paper is a continuation of the author's paper [in Semigroup Forum 48, No. 2, 180-192 (1994; Zbl 0797.20048)]. A completely regular semigroup is a union of groups. For a completely regular semigroup \(S\) let \(C^*(S)\) be the least full and self-conjugate subsemigroup of \(S\). Let \(A\) be a variety of completely regular semigroups and let \(AC^*\) be the class of all completely regular semigroups \(S\) such that \(C^*(S)\in A\). Then \(C^*\) is an operator on the lattice \(L\) of all varieties of completely regular semigroups. In the paper this operator \(C^*\) is studied. It is shown, that \(C^*\) is infinite. This yields that the Mal'cev product is not associative on \(L\). Several other lattice theoretic properties of \(C^*\) are investigated.