On critical $\Omega$-fibered formations of finite groups

M. M. Sorokina ; M. A. Korpacheva

Diskretnaya Matematika, Tome 18 (2006) no. 1, pp. 106-115

Résumé

Let $\mathfrak H$ be a class of finite groups. An $\Omega$-foliated formation of finite groups $\mathfrak F$ with direction $\varphi$ is called a minimal $\Omega$-foliated non-$\mathfrak H$-formation $\varphi$, or a ${\mathfrak H}_{\Omega \varphi}$-critical formation if $\mathfrak F \nsubseteq \mathfrak H$, but all proper $\Omega$-foliated subformations with direction $\varphi$ in $\mathfrak F$ are contained in the class $\mathfrak H$. In this paper we give a complete description of the structure of minimal $\Omega$-foliated non-$\mathfrak H$-formations with $br$-direction $\varphi$ satisfying the condition $\varphi\leq\varphi_{3}$.