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 PFMT, 2019, Issue 2(39), Pages 61–65 (Mi pfmt638)

MATHEMATICS

On the intersections of generalized projectors with the products of normal subgroups of finite groups

T. I. Vasilyevaab

a F. Scorina Gomel State University
b Belarusian State University of Transport, Gomel

Abstract: The factorization properties of the $\mathfrak{F}^\omega$-projector introduced by V. A. Vedernikov and M. M. Sorokina in 2016 ($\omega$ is a non-empty set of primes and $\mathfrak{F}$ is a non-empty class of groups) were investigated. Necessary and sufficient conditions are found for the equality $N_1N_2 \cap H = (N_1 \cap H)(N_2 \cap H)$ for any $\mathfrak{F}^\omega$-projector $H$ and any normal $\omega$-subgroups $N_1$ and $N_2$ of $G$, where $G$ is an extension of the $\omega$-group with the help of an $\mathfrak{F}$-group.

Keywords: finite group, $\mathfrak{F}^\omega$-projector, $\omega$-saturated formation, $\omega$-primitive closed homomorph.

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UDC: 512.542

Citation: T. I. Vasilyeva, “On the intersections of generalized projectors with the products of normal subgroups of finite groups”, PFMT, 2019, no. 2(39), 61–65

Citation in format AMSBIB
\Bibitem{Vas19} \by T.~I.~Vasilyeva \paper On the intersections of generalized projectors with the products of normal subgroups of finite groups \jour PFMT \yr 2019 \issue 2(39) \pages 61--65 \mathnet{http://mi.mathnet.ru/pfmt638}