LAUSR

It is known that the monoid wreath product of any two semigroup varieties that are atoms in the lattice of all semigroup varieties may have a finite as well as an infinite lattice of subvarieties. If this lattice is finite, then as a rule it has at most eleven elements. This was proved in a paper of the author in 2007. The exclusion is the monoid wreath product Sl w N2 of the variety of semilattices and the variety of semigroups with zero multiplication. The number of elements of the lattice L(Sl w N2) of subvarieties of Sl w N2 is still unknown. In our paper, we show that the lattice L(Sl w N2) contains no less than 33 elements. In addition, we give some exponential upper bound of the cardinality of this lattice.