Finite groups in which normality is a transitive relation

摘要

Let G be a finite group. We say that G is a T 0-group, if its Frattini quotient group $G/Phi (G)$ is a T-group, where by a T-group we mean a group in which every subnormal subgroup is normal. We determine the structure of a non T 0-group G all of whose proper subgroups are T 0-groups.