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

Let be a variety of completely regular semigroups. DefineC^* to be the class of all completely regular semigroupsS whose least full and self-conjugate subsemigroupC^*(S) belongs to. ThenC^* is an operator on the lattice of varieties of completely regular semigroups. In this note we show that the order ofC^* is infinite. This fact yields that the Mal'cev project is not associative on. We describe(C^*)¹, andi 0, in terms of -invariant normal subgroups of the free group over a countably infinite set. The lattice theoretic properties ofC^* are also studied.Presented by W. Taylor.