On Shemetkov’s problem of describing critical formations in the class of τ-closed σ-local formations - Skrundz, Valentina V.; Safonova, Inna N. (Journal of the Belarusian State University. Mathematics and Informatics, 2026)
The critical τ-closed σ-local formations of finite groups are studied, where σ is some partition of the set of all primes P, τ is an arbitrary subgroup functor. A description of minimal τ-closed σ-local non-H-formations is obtained for an arbitrary σ-local formation of classical type, i. e. a σ-local formation that has a σ-local definition all of whose non-Abelian values are σ-local formations. Thus, the problem of describing critical formations in the class of τ-closed σ-local formations proposed by L. A. Shemetkov (1980) is solved.