Finite groups with formational subnormal strictly 2-maximal subgroups

Abstract

Let be a subgroup-closed saturated Š-formation containing all nilpotent groups and let G be a group such that We prove that the requirement of -subnormality of all strictly 2-maximal subgroups coincides with the requirement of subnormality of all 2-maximal subgroups and is equivalent to G is a non-nilpotent group all of whose proper subgroups are abelian.