The Kegel – Shemetkov Problem on Lattices of Generalized Subnormal Subgroups of Finite Groups

We study into formations $\mathfrak F$ for which the set of all $\mathfrak F$-subnormal ($\mathfrak F$-accessible) subgroups form a sublattice of the lattice of all subgroups in every finite group. A constructive description of all soluble hereditary formations of finite groups with given properties is furnished.