The critical $\omega$-foliated $\tau$-closed formations of finite groups

M. A. Korpacheva ; M. M. Sorokina

Diskretnaya Matematika, Tome 23 (2011) no. 1, pp. 94-101

Résumé

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.