On the existence of H 𝜏σ -critical formations of finite groups

The 𝜏 -closed σ-local formations of finite groups are studied, where σ is some partition of the set of all primes, 𝜏 is an arbitrary subgroup functor. The question of the existence of 𝜏 Hσ -critical formations is investigated, i. e., such 𝜏 -closed σ-local formations L H ⊆ for which all proper 𝜏 -closed σ-local subformations are contained in the class of groups H. It is proved that if H is a σ-local formation of classical type, then every 𝜏 -closed σ-local formation F H ⊆ has at least one H 𝜏 σ - critical subformation.