FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 2, PAGES 201-221

**A generalization of the first Malcev theorem on nilpotent semigroups
and nilpotency of the wreath product of semigroups**

A. V. Tishchenko

Abstract

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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.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k112/k11209h.htm

Last modified: March 6, 2012