The critical ω-foliated τ-closed formations of finite groups

Abstract

Let be a class of finite groups, τ be a subgroup functor; an ω-foliated τ-closed formation of finite groups 𝔉 with direction δ is called the minimal ω-foliated τ-closed non--formation with direction δ, or, in other words, ωτδ-critical formation if 𝔉 ⊈ , but all proper ω-foliated τ-closed subformations with direction δ in 𝔉 are contained in the class . In this paper we investigate the structure of the minimal ω-foliated τ-closed non--formations with bp-direction δ satisfying the condition δ ≤ δ3 in the case where τ is a regular δ-radical subgroup functor.