
MATHEMATICS
On the intersections of generalized projectors with the products of normal subgroups of finite groups
T. I. Vasilyeva^{ab} ^{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 nonempty set of primes and $\mathfrak{F}$ is a nonempty 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 Received: 03.04.2019
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 6165
\mathnet{http://mi.mathnet.ru/pfmt638}
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