A generalization of the first Malcev theorem on nilpotent semigroups and nilpotency of the wreath product of semigroups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 2, pp. 201-221
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We describe all [0-]simple semigroups that are nilpotent in the sense of Malcev. This generalizes the first Malcev theorem on nilpotent (in the sense of Malcev) semigroups. It is proved that if the extended standard wreath product of semigroups is nilpotent in the sense of Malcev and the passive semigroup is not nilpotent, then the active semigroup of the wreath product is a finite nilpotent group. In addition to that, the passive semigroup is uniform periodic. There are found necessary and sufficient conditions under which the extended standard wreath product of semigroups is nilpotent in the sense of Malcev in the case where each of the semigroups of the wreath product generates a variety of finite step.
@article{FPM_2012_17_2_a8,
author = {A. V. Tishchenko},
title = {A generalization of the first {Malcev} theorem on nilpotent semigroups and nilpotency of the wreath product of semigroups},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {201--221},
publisher = {mathdoc},
volume = {17},
number = {2},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a8/}
}
TY - JOUR AU - A. V. Tishchenko TI - A generalization of the first Malcev theorem on nilpotent semigroups and nilpotency of the wreath product of semigroups JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2012 SP - 201 EP - 221 VL - 17 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a8/ LA - ru ID - FPM_2012_17_2_a8 ER -
%0 Journal Article %A A. V. Tishchenko %T A generalization of the first Malcev theorem on nilpotent semigroups and nilpotency of the wreath product of semigroups %J Fundamentalʹnaâ i prikladnaâ matematika %D 2012 %P 201-221 %V 17 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a8/ %G ru %F FPM_2012_17_2_a8
A. V. Tishchenko. A generalization of the first Malcev theorem on nilpotent semigroups and nilpotency of the wreath product of semigroups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 2, pp. 201-221. http://geodesic.mathdoc.fr/item/FPM_2012_17_2_a8/