Geodesic
On the lattice of subvarieties of the wreath product the variety of semilattices and the variety of semigroups with zero multiplication
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 6, pp. 191-212 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is known that the monoid wreath product of any semigroup varieties that are atoms in the lattice of all semigroup varieties mays 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 $\mathbf{Sl}\mathrm w\mathbf N_2$ of the variety of semilattices and the variety of semigroups with zero multiplication. The number of elements of the lattice $L(\mathbf{Sl}\mathrm w\mathbf N_2)$ of subvarieties of $\mathbf{Sl}\mathrm w\mathbf N_2$ is still unknown. In our paper, we show that the lattice $L(\mathbf{Sl}\mathrm w\mathbf N_2)$ contains no less than 33 elements. In addition, we give some exponential upper bound of the cardinality of this lattice. 
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A. V. Tishchenko. On the lattice of subvarieties of the wreath product the variety of semilattices and the variety of semigroups with zero multiplication. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 6, pp. 191-212. http://geodesic.mathdoc.fr/item/FPM_2014_19_6_a8/

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