On minimal \(\omega\)-composition non-\(\frak H\)-formations

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 \(G\).