Intersection of subnormal subgroups

Definition
A subgroup of a group is termed an intersection of subnormal subgroups if it satisfies the following equivalent conditions:


 * It can be expressed as the intersection of a descending chain of defining ingredient::subnormal subgroups.
 * It can be expressed as an intersection of subnormal subgroups.

Note that since subnormality of fixed depth is closed under arbitrary intersections, these two definitions are equivalent.

Stronger properties

 * Weaker than::Normal subgroup
 * Weaker than::Subnormal subgroup

Weaker properties

 * Stronger than::Descendant subgroup