MINIMAL τ-CLOSED σ-LOCAL NON-H-FORMATIONS OF FINITE GROUPS

Abstract

A description of minimal t-closed s-local non-H-formations is obtained for an arbitrary s-local formation H of classical type, i. e., a s-local formation that has such a s-local definition, all non-abelian values of which are s-local for mations. This result provides a solution to L. A. Shemetkov’s problem (1980) on describing critical formations in the class of t-closed s-local formations, where s is some partition of the set of all prime numbers, t is an arbitrary subgroup functor. Keyword: finite group, formation s-function, s-local formation, subgroup functor, t-closed formation, critical s-local formation, formation of classical type.