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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 2012, Volume 17, Issue 2, Pages 201–221 (Mi fpm1408)

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

A. V. Tishchenko

Financial University under the Government of the Russian Federation

Abstract: 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.

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English version:
Journal of Mathematical Sciences (New York), 2012, 186:4, 667–681

Document Type: Article
UDC: 512.532

Citation: A. V. Tishchenko, “A generalization of the first Malcev theorem on nilpotent semigroups and nilpotency of the wreath product of semigroups”, Fundam. Prikl. Mat., 17:2 (2012), 201–221; J. Math. Sci., 186:4 (2012), 667–681

Citation in format AMSBIB
\Bibitem{Tis12} \by A.~V.~Tishchenko \paper A generalization of the first Malcev theorem on nilpotent semigroups and nilpotency of the wreath product of semigroups \jour Fundam. Prikl. Mat. \yr 2012 \vol 17 \issue 2 \pages 201--221 \mathnet{http://mi.mathnet.ru/fpm1408} \transl \jour J. Math. Sci. \yr 2012 \vol 186 \issue 4 \pages 667--681 \crossref{https://doi.org/10.1007/s10958-012-1013-y} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866504863}