A SUBGROUP LATTICE OF A FINITE SOLUBLE GROUP

Abstract A subgroup R of a finite group G is called weakly subnormal in G if R is not subnormal in G but it is subnormal in every proper overgroup of R in G . In this paper, weak subnormality is used to construct a subgroup lattice of a finite soluble group containing the lattice of all subnormal subgroups. A new characterisation of Schmidt groups is also obtained: they are exactly those groups with all subgroups subnormal or weakly subnormal.