Hereditary critical \(\Omega\)-composition formations (Q2754828)

Let \(\theta\) be a non-empty set of formations and let \(\mathfrak H\) be a class of groups. A \(\theta\)-formation \(\mathfrak F\) is called \({\mathfrak H}_\theta\)-critical if \({\mathfrak F}\not\subseteq{\mathfrak H}\), but every proper \(\theta\)-subformation of the formation \(\mathfrak F\) is contained in \(\mathfrak H\). The authors deal with the problem concerning the structure of \({\mathfrak H}_\theta\)-critical formations \(\mathfrak F\) for some class \(\mathfrak H\) of groups and non-empty set \(\theta\) of formations. The problem is solved for hereditary \(\Omega\)-composition formations. All possible \({\mathfrak H}_\theta\)-critical formations are listed in this case in three theorems.