On groups with formational subnormal Sylow subgroups

Abstract

We investigate a finite group G with F-subnormal Sylow subgroups, where F is a subgroup-closed formation and A1A⊆F⊆NA. We prove that G is soluble and the derived subgroup of each metanilpotent subgroup is nilpotent. We also describe the structure of groups in which every Sylow subgroup is F-subnormal or F-abnormal.