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RESEARCH ARTICLE

On minimal $\omega$-composition non-$\frak H$-formations

Liudmila I. Belous, Vadim M. Sel'kin

Gomel State University of F. Skorina, Belarus, 246019, Gomel, Sovetskaya Str., 104

Abstract: Let $\frak{H}$ be some class of groups. A formation $\frak{F}$ is called a minimal $\tau$-closed $\omega$-composition non-$\frak{H}$-formation [1] if $\frak{F}\nsubseteq\frak{H}$ but $\frak{F}_1\subseteq\frak{H}$ for all proper $\tau$-closed $\omega$-composition subformations $\frak{F}_1$ of $\frak{F}$. In this paper we describe the minimal $\tau$-closed $\omega$-composition non-$\frak{H}$-formations, where $\frak H$ is a 2-multiply local formation and $\tau$ is a subgroup functor such that for any group $G$ all subgroups from $\tau(G)$ are subnormal in $G$.

Keywords: formation, $\tau$-closed $\omega$-composition, satellite.

MSC: 20D20

Received: 06.05.2006
Revised: 10.04.2007

Language: English

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