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This article is cited in 3 scientific papers (total in 3 papers)
The critical $\omega$-foliated $\tau$-closed formations of finite groups
M. A. Korpacheva, M. M. Sorokina
Abstract:
Let $\mathfrak H$ be a class of finite groups, $\tau$ be a subgroup functor; an $\omega$-foliated $\tau$-closed formation of finite groups $\mathfrak F$ with direction $\delta$ is called the minimal $\omega$-foliated $\tau$-closed non-$\mathfrak H$-formation with direction $\delta$, or, in other words, $\mathfrak H_{\omega\tau\delta}$-critical formation if $\mathfrak F\not\subseteq\mathfrak H$, but all proper $\omega$-foliated $\tau$-closed subformations with direction $\delta$ in $\mathfrak F$ are contained in the class $\mathfrak H$. In this paper we investigate the structure of the minimal $\omega$-foliated $\tau$-closed non-$\mathfrak H$-formations with $bp$-direction $\delta$ satisfying the condition $\delta\le\delta_3$ in the case where $\tau$ is a regular $\delta$-radical subgroup functor.
Received: 12.11.2008 Revised: 07.06.2009
Citation:
M. A. Korpacheva, M. M. Sorokina, “The critical $\omega$-foliated $\tau$-closed formations of finite groups”, Diskr. Mat., 23:1 (2011), 94–101; Discrete Math. Appl., 21:1 (2011), 69–77
Linking options:
https://www.mathnet.ru/eng/dm1133https://doi.org/10.4213/dm1133 https://www.mathnet.ru/eng/dm/v23/i1/p94
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