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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 3, Pages 316–320 (Mi timm991)  

On the $\mathfrak F$-residual of the direct product of finite groups

L. A. Shemetkov

Francisk Skorina Gomel State University
References:
Abstract: Let $\pi$ be a subset of the set $\mathbb P$ of all primes, and let $\pi'=\mathbb P\backslash\pi$. A formation $\mathfrak F$ is called $\pi'$-saturated if $G/O_{\pi'}(\Phi(G))\in\mathfrak F$ implies $G\in\mathfrak F$. If $\mathfrak F$ is a nonempty $\pi'$-saturated formation of $\pi$-soluble groups, then it is proved that $(A\otimes B)^\mathfrak F=A^\mathfrak F\otimes B^\mathfrak F$ for any finite groups $A$ and $B$. In the case $\pi=\mathbb P$, this result was proved by K. Doerk and T. Hawkes in 1978.
Keywords: finite group, direct product, formation, $\mathfrak F$-residual.
Received: 10.12.2012
Bibliographic databases:
Document Type: Article
UDC: 512.542.6
Language: Russian
Citation: L. A. Shemetkov, “On the $\mathfrak F$-residual of the direct product of finite groups”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 316–320
Citation in format AMSBIB
\Bibitem{She13}
\by L.~A.~Shemetkov
\paper On the $\mathfrak F$-residual of the direct product of finite groups
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 3
\pages 316--320
\mathnet{http://mi.mathnet.ru/timm991}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3363326}
\elib{https://elibrary.ru/item.asp?id=20235000}
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