Some properties of finite groups with some (semi-pp-)cover-avoiding subgroups

In recent years, in trying to generalize the normality of subgroups, (semi-)(pp-)cover-avoiding subgroups were defined. Some valuable results on the structure of a finite group were set up, provided that its subgroups have the cover-avoiding property, semi-cover-avoiding property or semi-pp-cover-avoiding property. Since whether a subgroup covers or avoids in a group is connected to the chief series of the group, the results look interesting. Here the authors discuss the connection between the structure of a finite group and its (semi-)(pp-)cover-avoiding maximal or minimal subgroups, and obtain some sufficient conditions for a group being pp-nilpotent or supersolvable.