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Tr. Inst. Mat., 2008, Volume 16, Number 1, Pages 67–72 (Mi timb57)  

This article is cited in 1 scientific paper (total in 1 paper)

On the existence of minimal $\tau$-closed totally saturated non-$\mathfrak H$-formations

V. G. Safonov

Francisk Skorina Gomel State University

Abstract: The article deals with finite groups. A $\tau$-closed totally saturated formation $\mathfrak F$ is called a minimal $\tau$-closed totally saturated non-$\mathfrak H$-formation (or an $\mathfrak H_\infty^\tau$-critical formation) if $\mathfrak F\not\subseteq\mathfrak H$, but all proper $\tau$-closed totally saturated subformations of $\mathfrak F$ are contained in $\mathfrak H$. Theorem. Let $\mathfrak F$ and $\mathfrak H$ be $\tau$-closed totally saturated formations, $\mathfrak F\not\subseteq\mathfrak H.$ Then $\mathfrak F$ has at least one minimal $\tau$-closed totally saturated non-$\mathfrak H$-formation.

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UDC: 512.542
Received: 03.01.2008

Citation: V. G. Safonov, “On the existence of minimal $\tau$-closed totally saturated non-$\mathfrak H$-formations”, Tr. Inst. Mat., 16:1 (2008), 67–72

Citation in format AMSBIB
\Bibitem{Saf08}
\by V.~G.~Safonov
\paper On the existence of minimal $\tau$-closed totally saturated non-$\mathfrak H$-formations
\jour Tr. Inst. Mat.
\yr 2008
\vol 16
\issue 1
\pages 67--72
\mathnet{http://mi.mathnet.ru/timb57}


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    This publication is cited in the following articles:
    1. V. P. Burichenko, “Nekotorye voprosy konechnosti dlya formatsii”, Tr. In-ta matem., 21:1 (2013), 15–24  mathnet
  • Труды Института математики
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