Description of finite solvable minimal non-\({\mathcal F}\)-groups for an arbitrary totally local formation \({\mathcal F}\) (Q1825273)

Let \({\mathcal M}({\mathcal F})\) be the set of all minimal non \({\mathcal F}\)-groups, i.e. groups not lying in some class of groups \({\mathcal F}\) all proper subgroups of which lie in \({\mathcal F}\). The paper describes solvable groups in \({\mathcal M}({\mathcal F})\) for an arbitrary totally local formation \({\mathcal F}\). It turns out that all such groups are two-generated. Special cases of this problem have been studied previously.