Geodesic
A wreath product of semigroups and varieties of finite index
Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 3, pp. 889-902 
A. V. Tishchenko. A wreath product of semigroups and varieties of finite index. Fundamentalʹnaâ i prikladnaâ matematika, Tome 6 (2000) no. 3, pp. 889-902. http://geodesic.mathdoc.fr/item/FPM_2000_6_3_a18/
@article{FPM_2000_6_3_a18,
     author = {A. V. Tishchenko},
     title = {A~wreath product of semigroups and varieties of finite index},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {889--902},
     year = {2000},
     volume = {6},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2000_6_3_a18/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We have found the necessary and sufficient conditions on semigroups under which their extended standard wreath product generates a variety of finite index. Further, the similar problem is solved for varieties of completely simple semigroups. Finally, the necessary and sufficient conditions on monoid $S$ are found under which the endomorphism monoid of a free left act over $S$ generates a variety of finite index.