Group in which every cyclic subgroup is 2-subnormal
A group in which every cyclic subgroup is 2-subnormal is a group with the property that every cyclic subgroup (i.e., the subgroup generated by any subset of the group) of the group is a 2-subnormal subgroup.
In terms of the subgroup property collapse operator
This group property can be defined in terms of the collapse of two subgroup properties. In other words, a group satisfies this group property if and only if every subgroup of it satisfying the first property (cyclic subgroup) satisfies the second property (cyclic 2-subnormal subgroup), and vice versa.
View other group properties obtained in this way
Relation with other properties
- Abelian group
- Dedekind group
- Group of nilpotence class two
- Group in which every subgroup is 2-subnormal