Products of F∗(G)-subnormal subgroups of finite groups

Abstract

A subgroup [Formula: see text] of a group [Formula: see text] is called [Formula: see text]-subnormal if it is subnormal in the product with the generalized Fitting subgroup [Formula: see text] of [Formula: see text]. All saturated formations [Formula: see text] that contain every group [Formula: see text] where [Formula: see text] and [Formula: see text] are [Formula: see text]-subnormal [Formula: see text]-subgroups are described. Moreover, if such formation [Formula: see text] is also normally hereditary, then every group [Formula: see text] where [Formula: see text] and [Formula: see text] are [Formula: see text]-subnormal quasi-[Formula: see text]-subgroups is a quasi-[Formula: see text]-group. The connection of above-mentioned formations to the lattice formations, GWP-formations and formations with the Kegel property is found.