On Finite Groups with Permutable Generalized Subnormal Subgroups

Abstract

We study the Kegel–Shemetkov problem of finding the classes of finite groups \( {\mathfrak F} \) such that, in any finite group, the product of permutable \( {\mathfrak F} \) -subnormal subgroups is a \( {\mathfrak F} \) -subnormal subgroup.