Finite groups with subgroups supersoluble or subnormal.
The paper studies the structure of finite groups whose non-subnormal subgroups lie in some subclasses of the class \(\mathcal U\) of finite supersoluble groups. These subclasses are \(\mathcal U\) itself, the class of PST-groups (i.e. groups in which the property of permuting with Sylow subgroups is transitive), the class of PT-groups (i.e. groups in which permutability is transitive) and the class of T-groups (i.e. groups in which normality of subgroups is transitive). For each of these classes the authors give a detailed description of the possible structure of such groups. They show that there is a complemented chief factor with complement in the given class and that it is easy to construct examples to show that a group with a complemented chief factor having a complement in the given class is not sufficient to ensure that all non-subnormal subgroups lie in the given class. The paper analyses the way in which a complement acts on the complemented chief factor and describes this action in enough detail to characterize the groups in each class.
scientific article; zbMATH DE number 5562709