Group in which any two normal subgroups are comparable
Definition
A group is said to be normal-comparable if any two normal subgroups of the group can be compared, or in other words, if its lattice of normal subgroups is a totally ordered set. In other words, given any two normal subgroups of the group, one of them must lie completely inside the other.
In terms of the comparability operator
This group property is obtained by applying the comparability operator to the subgroup property of normality.
Relation with other properties
Stronger properties
Weaker properties
- Characteristic-comparable group
- Group in which every normal subgroup is characteristic, at least for a finite group